Update the HOL4 proofs for the last *release* version of HOL4

10 files changed, 468 insertions, 470 deletions

diff --git a/.gitignore b/.gitignore
index 11ac64b9..2d668039 100644
--- a/.gitignore
+++ b/.gitignore
@@ -61,6 +61,10 @@ tests/fstar/misc/obj/
 .HOLMK
 .hollogs
 .holobjs
+*.dat
+*.ui
+*.uo
+*Theory.sml
 
 # Misc
 /fstar-tests
diff --git a/backends/hol4/divDefLibTestTheory.sig b/backends/hol4/divDefLibTestTheory.sig
index d8cc4ab5..2df28a2f 100644
--- a/backends/hol4/divDefLibTestTheory.sig
+++ b/backends/hol4/divDefLibTestTheory.sig
@@ -53,7 +53,6 @@ sig
     val tree_distinct : thm
     val tree_induction : thm
     val tree_nchotomy : thm
-    val tree_size_eq : thm
   
   val divDefLibTest_grammars : type_grammar.grammar * term_grammar.grammar
 (*
@@ -434,10 +433,6 @@ sig
       
       ⊢ ∀tt. (∃a. tt = TLeaf a) ∨ ∃n. tt = TNode n
    
-   [tree_size_eq]  Theorem
-      
-      ⊢ tree1_size f = list_size (tree_size f)
-   
    
 *)
 end
diff --git a/backends/hol4/divDefNoFixLibTestTheory.sig b/backends/hol4/divDefNoFixLibTestTheory.sig
index 999cf543..6c8f373c 100644
--- a/backends/hol4/divDefNoFixLibTestTheory.sig
+++ b/backends/hol4/divDefNoFixLibTestTheory.sig
@@ -5,12 +5,12 @@ sig
   (*  Definitions  *)
     val even___E_def : thm
     val even___P_def : thm
-    val even___fuel0_def_UNION_extract0 : thm
-    val even___fuel0_def_UNION_extract1 : thm
-    val even___fuel0_def_UNION_primitive : thm
-    val even___fuel_def_UNION_extract0 : thm
-    val even___fuel_def_UNION_extract1 : thm
-    val even___fuel_def_UNION_primitive : thm
+    val even___fuel0_UNION_extract0_def : thm
+    val even___fuel0_UNION_extract1_def : thm
+    val even___fuel0_UNION_primitive_def : thm
+    val even___fuel_UNION_extract0_def : thm
+    val even___fuel_UNION_extract1_def : thm
+    val even___fuel_UNION_primitive_def : thm
     val even_def : thm
     val list_t_TY_DEF : thm
     val list_t_case_def : thm
@@ -56,17 +56,17 @@ sig
       ⊢ ∀i $var$($n).
           even___P i $var$($n) ⇔ ¬is_diverge (even___fuel0 $var$($n) i)
    
-   [even___fuel0_def_UNION_extract0]  Definition
+   [even___fuel0_UNION_extract0_def]  Definition
       
-      ⊢ ∀x x0. even___fuel0 x x0 = even___fuel0_def_UNION (INL (x,x0))
+      ⊢ ∀x x0. even___fuel0 x x0 = even___fuel0_UNION (INL (x,x0))
    
-   [even___fuel0_def_UNION_extract1]  Definition
+   [even___fuel0_UNION_extract1_def]  Definition
       
-      ⊢ ∀x x0. odd___fuel0 x x0 = even___fuel0_def_UNION (INR (x,x0))
+      ⊢ ∀x x0. odd___fuel0 x x0 = even___fuel0_UNION (INR (x,x0))
    
-   [even___fuel0_def_UNION_primitive]  Definition
+   [even___fuel0_UNION_primitive_def]  Definition
       
-      ⊢ even___fuel0_def_UNION =
+      ⊢ even___fuel0_UNION =
         WFREC
           (@R. WF R ∧
                (∀i $var$($n) $var$($m).
@@ -75,7 +75,7 @@ sig
                ∀i $var$($n) $var$($m).
                  $var$($n) = SUC $var$($m) ∧ i ≠ 0 ⇒
                  R (INL ($var$($m),i − 1)) (INR ($var$($n),i)))
-          (λeven___fuel0_def_UNION a.
+          (λeven___fuel0_UNION a.
                case a of
                  INL ($var$($n),i) =>
                    I
@@ -85,9 +85,7 @@ sig
                         if i = 0 then do b <- Return T; Return b od
                         else
                           do
-                            b <-
-                              even___fuel0_def_UNION
-                                (INR ($var$($m),i − 1));
+                            b <- even___fuel0_UNION (INR ($var$($m),i − 1));
                             Return b
                           od)
                | INR ($var$($n'),i') =>
@@ -98,22 +96,21 @@ sig
                       if i' = 0 then do b <- Return F; Return b od
                       else
                         do
-                          b <-
-                            even___fuel0_def_UNION (INL ($var$($m),i' − 1));
+                          b <- even___fuel0_UNION (INL ($var$($m),i' − 1));
                           Return b
                         od))
    
-   [even___fuel_def_UNION_extract0]  Definition
+   [even___fuel_UNION_extract0_def]  Definition
       
-      ⊢ ∀x x0. even___fuel x x0 = even___fuel_def_UNION (INL (x,x0))
+      ⊢ ∀x x0. even___fuel x x0 = even___fuel_UNION (INL (x,x0))
    
-   [even___fuel_def_UNION_extract1]  Definition
+   [even___fuel_UNION_extract1_def]  Definition
       
-      ⊢ ∀x x0. odd___fuel x x0 = even___fuel_def_UNION (INR (x,x0))
+      ⊢ ∀x x0. odd___fuel x x0 = even___fuel_UNION (INR (x,x0))
    
-   [even___fuel_def_UNION_primitive]  Definition
+   [even___fuel_UNION_primitive_def]  Definition
       
-      ⊢ even___fuel_def_UNION =
+      ⊢ even___fuel_UNION =
         WFREC
           (@R. WF R ∧
                (∀i $var$($n) $var$($m).
@@ -122,7 +119,7 @@ sig
                ∀i $var$($n) $var$($m).
                  $var$($n) = SUC $var$($m) ∧ i ≠ 0 ⇒
                  R (INL ($var$($m),i − 1)) (INR ($var$($n),i)))
-          (λeven___fuel_def_UNION a.
+          (λeven___fuel_UNION a.
                case a of
                  INL ($var$($n),i) =>
                    I
@@ -130,14 +127,14 @@ sig
                         0 => Diverge
                       | SUC $var$($m) =>
                         if i = 0 then Return T
-                        else even___fuel_def_UNION (INR ($var$($m),i − 1)))
+                        else even___fuel_UNION (INR ($var$($m),i − 1)))
                | INR ($var$($n'),i') =>
                  I
                    (case $var$($n') of
                       0 => Diverge
                     | SUC $var$($m) =>
                       if i' = 0 then Return F
-                      else even___fuel_def_UNION (INL ($var$($m),i' − 1))))
+                      else even___fuel_UNION (INL ($var$($m),i' − 1))))
    
    [even_def]  Definition
       
diff --git a/backends/hol4/primitivesTheory.sig b/backends/hol4/primitivesTheory.sig
index ae7f083d..6660b02d 100644
--- a/backends/hol4/primitivesTheory.sig
+++ b/backends/hol4/primitivesTheory.sig
@@ -359,195 +359,200 @@ sig
    
    [string] Parent theory of "primitives"
    
-   [isize_bounds]  Axiom
-      
-      [oracles: ] [axioms: isize_bounds] []
-      ⊢ isize_min ≤ i16_min ∧ i16_max ≤ isize_max
-   
-   [usize_bounds]  Axiom
-      
-      [oracles: ] [axioms: usize_bounds] [] ⊢ u16_max ≤ usize_max
-   
-   [isize_to_int_bounds]  Axiom
+   [i128_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: isize_to_int_bounds] []
-      ⊢ ∀n. isize_min ≤ isize_to_int n ∧ isize_to_int n ≤ isize_max
+      [oracles: ] [axioms: i128_to_int_bounds] []
+      ⊢ ∀n. i128_min ≤ i128_to_int n ∧ i128_to_int n ≤ i128_max
    
-   [i8_to_int_bounds]  Axiom
+   [i128_to_int_int_to_i128]  Axiom
       
-      [oracles: ] [axioms: i8_to_int_bounds] []
-      ⊢ ∀n. i8_min ≤ i8_to_int n ∧ i8_to_int n ≤ i8_max
+      [oracles: ] [axioms: i128_to_int_int_to_i128] []
+      ⊢ ∀n. i128_min ≤ n ∧ n ≤ i128_max ⇒ i128_to_int (int_to_i128 n) = n
    
    [i16_to_int_bounds]  Axiom
       
       [oracles: ] [axioms: i16_to_int_bounds] []
       ⊢ ∀n. i16_min ≤ i16_to_int n ∧ i16_to_int n ≤ i16_max
    
+   [i16_to_int_int_to_i16]  Axiom
+      
+      [oracles: ] [axioms: i16_to_int_int_to_i16] []
+      ⊢ ∀n. i16_min ≤ n ∧ n ≤ i16_max ⇒ i16_to_int (int_to_i16 n) = n
+   
    [i32_to_int_bounds]  Axiom
       
       [oracles: ] [axioms: i32_to_int_bounds] []
       ⊢ ∀n. i32_min ≤ i32_to_int n ∧ i32_to_int n ≤ i32_max
    
+   [i32_to_int_int_to_i32]  Axiom
+      
+      [oracles: ] [axioms: i32_to_int_int_to_i32] []
+      ⊢ ∀n. i32_min ≤ n ∧ n ≤ i32_max ⇒ i32_to_int (int_to_i32 n) = n
+   
    [i64_to_int_bounds]  Axiom
       
       [oracles: ] [axioms: i64_to_int_bounds] []
       ⊢ ∀n. i64_min ≤ i64_to_int n ∧ i64_to_int n ≤ i64_max
    
-   [i128_to_int_bounds]  Axiom
+   [i64_to_int_int_to_i64]  Axiom
       
-      [oracles: ] [axioms: i128_to_int_bounds] []
-      ⊢ ∀n. i128_min ≤ i128_to_int n ∧ i128_to_int n ≤ i128_max
+      [oracles: ] [axioms: i64_to_int_int_to_i64] []
+      ⊢ ∀n. i64_min ≤ n ∧ n ≤ i64_max ⇒ i64_to_int (int_to_i64 n) = n
    
-   [usize_to_int_bounds]  Axiom
+   [i8_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: usize_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ usize_to_int n ∧ usize_to_int n ≤ usize_max
+      [oracles: ] [axioms: i8_to_int_bounds] []
+      ⊢ ∀n. i8_min ≤ i8_to_int n ∧ i8_to_int n ≤ i8_max
    
-   [u8_to_int_bounds]  Axiom
+   [i8_to_int_int_to_i8]  Axiom
       
-      [oracles: ] [axioms: u8_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ u8_to_int n ∧ u8_to_int n ≤ u8_max
+      [oracles: ] [axioms: i8_to_int_int_to_i8] []
+      ⊢ ∀n. i8_min ≤ n ∧ n ≤ i8_max ⇒ i8_to_int (int_to_i8 n) = n
    
-   [u16_to_int_bounds]  Axiom
+   [int_to_i128_i128_to_int]  Axiom
       
-      [oracles: ] [axioms: u16_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ u16_to_int n ∧ u16_to_int n ≤ u16_max
+      [oracles: ] [axioms: int_to_i128_i128_to_int] []
+      ⊢ ∀i. int_to_i128 (i128_to_int i) = i
    
-   [u32_to_int_bounds]  Axiom
+   [int_to_i16_i16_to_int]  Axiom
       
-      [oracles: ] [axioms: u32_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ u32_to_int n ∧ u32_to_int n ≤ u32_max
+      [oracles: ] [axioms: int_to_i16_i16_to_int] []
+      ⊢ ∀i. int_to_i16 (i16_to_int i) = i
    
-   [u64_to_int_bounds]  Axiom
+   [int_to_i32_i32_to_int]  Axiom
       
-      [oracles: ] [axioms: u64_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ u64_to_int n ∧ u64_to_int n ≤ u64_max
+      [oracles: ] [axioms: int_to_i32_i32_to_int] []
+      ⊢ ∀i. int_to_i32 (i32_to_int i) = i
    
-   [u128_to_int_bounds]  Axiom
+   [int_to_i64_i64_to_int]  Axiom
       
-      [oracles: ] [axioms: u128_to_int_bounds] []
-      ⊢ ∀n. 0 ≤ u128_to_int n ∧ u128_to_int n ≤ u128_max
+      [oracles: ] [axioms: int_to_i64_i64_to_int] []
+      ⊢ ∀i. int_to_i64 (i64_to_int i) = i
    
-   [isize_to_int_int_to_isize]  Axiom
+   [int_to_i8_i8_to_int]  Axiom
       
-      [oracles: ] [axioms: isize_to_int_int_to_isize] []
-      ⊢ ∀n. isize_min ≤ n ∧ n ≤ isize_max ⇒
-            isize_to_int (int_to_isize n) = n
+      [oracles: ] [axioms: int_to_i8_i8_to_int] []
+      ⊢ ∀i. int_to_i8 (i8_to_int i) = i
    
-   [i8_to_int_int_to_i8]  Axiom
+   [int_to_isize_isize_to_int]  Axiom
       
-      [oracles: ] [axioms: i8_to_int_int_to_i8] []
-      ⊢ ∀n. i8_min ≤ n ∧ n ≤ i8_max ⇒ i8_to_int (int_to_i8 n) = n
+      [oracles: ] [axioms: int_to_isize_isize_to_int] []
+      ⊢ ∀i. int_to_isize (isize_to_int i) = i
    
-   [i16_to_int_int_to_i16]  Axiom
+   [int_to_u128_u128_to_int]  Axiom
       
-      [oracles: ] [axioms: i16_to_int_int_to_i16] []
-      ⊢ ∀n. i16_min ≤ n ∧ n ≤ i16_max ⇒ i16_to_int (int_to_i16 n) = n
+      [oracles: ] [axioms: int_to_u128_u128_to_int] []
+      ⊢ ∀i. int_to_u128 (u128_to_int i) = i
    
-   [i32_to_int_int_to_i32]  Axiom
+   [int_to_u16_u16_to_int]  Axiom
       
-      [oracles: ] [axioms: i32_to_int_int_to_i32] []
-      ⊢ ∀n. i32_min ≤ n ∧ n ≤ i32_max ⇒ i32_to_int (int_to_i32 n) = n
+      [oracles: ] [axioms: int_to_u16_u16_to_int] []
+      ⊢ ∀i. int_to_u16 (u16_to_int i) = i
    
-   [i64_to_int_int_to_i64]  Axiom
+   [int_to_u32_u32_to_int]  Axiom
       
-      [oracles: ] [axioms: i64_to_int_int_to_i64] []
-      ⊢ ∀n. i64_min ≤ n ∧ n ≤ i64_max ⇒ i64_to_int (int_to_i64 n) = n
+      [oracles: ] [axioms: int_to_u32_u32_to_int] []
+      ⊢ ∀i. int_to_u32 (u32_to_int i) = i
    
-   [i128_to_int_int_to_i128]  Axiom
+   [int_to_u64_u64_to_int]  Axiom
       
-      [oracles: ] [axioms: i128_to_int_int_to_i128] []
-      ⊢ ∀n. i128_min ≤ n ∧ n ≤ i128_max ⇒ i128_to_int (int_to_i128 n) = n
+      [oracles: ] [axioms: int_to_u64_u64_to_int] []
+      ⊢ ∀i. int_to_u64 (u64_to_int i) = i
    
-   [usize_to_int_int_to_usize]  Axiom
+   [int_to_u8_u8_to_int]  Axiom
       
-      [oracles: ] [axioms: usize_to_int_int_to_usize] []
-      ⊢ ∀n. 0 ≤ n ∧ n ≤ usize_max ⇒ usize_to_int (int_to_usize n) = n
+      [oracles: ] [axioms: int_to_u8_u8_to_int] []
+      ⊢ ∀i. int_to_u8 (u8_to_int i) = i
    
-   [u8_to_int_int_to_u8]  Axiom
+   [int_to_usize_usize_to_int]  Axiom
       
-      [oracles: ] [axioms: u8_to_int_int_to_u8] []
-      ⊢ ∀n. 0 ≤ n ∧ n ≤ u8_max ⇒ u8_to_int (int_to_u8 n) = n
+      [oracles: ] [axioms: int_to_usize_usize_to_int] []
+      ⊢ ∀i. int_to_usize (usize_to_int i) = i
    
-   [u16_to_int_int_to_u16]  Axiom
+   [isize_bounds]  Axiom
       
-      [oracles: ] [axioms: u16_to_int_int_to_u16] []
-      ⊢ ∀n. 0 ≤ n ∧ n ≤ u16_max ⇒ u16_to_int (int_to_u16 n) = n
+      [oracles: ] [axioms: isize_bounds] []
+      ⊢ isize_min ≤ i16_min ∧ i16_max ≤ isize_max
    
-   [u32_to_int_int_to_u32]  Axiom
+   [isize_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: u32_to_int_int_to_u32] []
-      ⊢ ∀n. 0 ≤ n ∧ n ≤ u32_max ⇒ u32_to_int (int_to_u32 n) = n
+      [oracles: ] [axioms: isize_to_int_bounds] []
+      ⊢ ∀n. isize_min ≤ isize_to_int n ∧ isize_to_int n ≤ isize_max
    
-   [u64_to_int_int_to_u64]  Axiom
+   [isize_to_int_int_to_isize]  Axiom
       
-      [oracles: ] [axioms: u64_to_int_int_to_u64] []
-      ⊢ ∀n. 0 ≤ n ∧ n ≤ u64_max ⇒ u64_to_int (int_to_u64 n) = n
+      [oracles: ] [axioms: isize_to_int_int_to_isize] []
+      ⊢ ∀n. isize_min ≤ n ∧ n ≤ isize_max ⇒
+            isize_to_int (int_to_isize n) = n
+   
+   [mk_vec_axiom]  Axiom
+      
+      [oracles: ] [axioms: mk_vec_axiom] []
+      ⊢ ∀l. len l ≤ usize_max ⇒ vec_to_list (mk_vec l) = l
+   
+   [u128_to_int_bounds]  Axiom
+      
+      [oracles: ] [axioms: u128_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ u128_to_int n ∧ u128_to_int n ≤ u128_max
    
    [u128_to_int_int_to_u128]  Axiom
       
       [oracles: ] [axioms: u128_to_int_int_to_u128] []
       ⊢ ∀n. 0 ≤ n ∧ n ≤ u128_max ⇒ u128_to_int (int_to_u128 n) = n
    
-   [int_to_i8_i8_to_int]  Axiom
-      
-      [oracles: ] [axioms: int_to_i8_i8_to_int] []
-      ⊢ ∀i. int_to_i8 (i8_to_int i) = i
-   
-   [int_to_i16_i16_to_int]  Axiom
+   [u16_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_i16_i16_to_int] []
-      ⊢ ∀i. int_to_i16 (i16_to_int i) = i
+      [oracles: ] [axioms: u16_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ u16_to_int n ∧ u16_to_int n ≤ u16_max
    
-   [int_to_i32_i32_to_int]  Axiom
+   [u16_to_int_int_to_u16]  Axiom
       
-      [oracles: ] [axioms: int_to_i32_i32_to_int] []
-      ⊢ ∀i. int_to_i32 (i32_to_int i) = i
+      [oracles: ] [axioms: u16_to_int_int_to_u16] []
+      ⊢ ∀n. 0 ≤ n ∧ n ≤ u16_max ⇒ u16_to_int (int_to_u16 n) = n
    
-   [int_to_i64_i64_to_int]  Axiom
+   [u32_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_i64_i64_to_int] []
-      ⊢ ∀i. int_to_i64 (i64_to_int i) = i
+      [oracles: ] [axioms: u32_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ u32_to_int n ∧ u32_to_int n ≤ u32_max
    
-   [int_to_i128_i128_to_int]  Axiom
+   [u32_to_int_int_to_u32]  Axiom
       
-      [oracles: ] [axioms: int_to_i128_i128_to_int] []
-      ⊢ ∀i. int_to_i128 (i128_to_int i) = i
+      [oracles: ] [axioms: u32_to_int_int_to_u32] []
+      ⊢ ∀n. 0 ≤ n ∧ n ≤ u32_max ⇒ u32_to_int (int_to_u32 n) = n
    
-   [int_to_isize_isize_to_int]  Axiom
+   [u64_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_isize_isize_to_int] []
-      ⊢ ∀i. int_to_isize (isize_to_int i) = i
+      [oracles: ] [axioms: u64_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ u64_to_int n ∧ u64_to_int n ≤ u64_max
    
-   [int_to_u8_u8_to_int]  Axiom
+   [u64_to_int_int_to_u64]  Axiom
       
-      [oracles: ] [axioms: int_to_u8_u8_to_int] []
-      ⊢ ∀i. int_to_u8 (u8_to_int i) = i
+      [oracles: ] [axioms: u64_to_int_int_to_u64] []
+      ⊢ ∀n. 0 ≤ n ∧ n ≤ u64_max ⇒ u64_to_int (int_to_u64 n) = n
    
-   [int_to_u16_u16_to_int]  Axiom
+   [u8_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_u16_u16_to_int] []
-      ⊢ ∀i. int_to_u16 (u16_to_int i) = i
+      [oracles: ] [axioms: u8_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ u8_to_int n ∧ u8_to_int n ≤ u8_max
    
-   [int_to_u32_u32_to_int]  Axiom
+   [u8_to_int_int_to_u8]  Axiom
       
-      [oracles: ] [axioms: int_to_u32_u32_to_int] []
-      ⊢ ∀i. int_to_u32 (u32_to_int i) = i
+      [oracles: ] [axioms: u8_to_int_int_to_u8] []
+      ⊢ ∀n. 0 ≤ n ∧ n ≤ u8_max ⇒ u8_to_int (int_to_u8 n) = n
    
-   [int_to_u64_u64_to_int]  Axiom
+   [usize_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_u64_u64_to_int] []
-      ⊢ ∀i. int_to_u64 (u64_to_int i) = i
+      [oracles: ] [axioms: usize_bounds] [] ⊢ u16_max ≤ usize_max
    
-   [int_to_u128_u128_to_int]  Axiom
+   [usize_to_int_bounds]  Axiom
       
-      [oracles: ] [axioms: int_to_u128_u128_to_int] []
-      ⊢ ∀i. int_to_u128 (u128_to_int i) = i
+      [oracles: ] [axioms: usize_to_int_bounds] []
+      ⊢ ∀n. 0 ≤ usize_to_int n ∧ usize_to_int n ≤ usize_max
    
-   [int_to_usize_usize_to_int]  Axiom
+   [usize_to_int_int_to_usize]  Axiom
       
-      [oracles: ] [axioms: int_to_usize_usize_to_int] []
-      ⊢ ∀i. int_to_usize (usize_to_int i) = i
+      [oracles: ] [axioms: usize_to_int_int_to_usize] []
+      ⊢ ∀n. 0 ≤ n ∧ n ≤ usize_max ⇒ usize_to_int (int_to_usize n) = n
    
    [vec_to_list_num_bounds]  Axiom
       
@@ -555,11 +560,6 @@ sig
       ⊢ ∀v. 0 ≤ LENGTH (vec_to_list v) ∧
             LENGTH (vec_to_list v) ≤ Num usize_max
    
-   [mk_vec_axiom]  Axiom
-      
-      [oracles: ] [axioms: mk_vec_axiom] []
-      ⊢ ∀l. len l ≤ usize_max ⇒ vec_to_list (mk_vec l) = l
-   
    [bind_def]  Definition
       
       ⊢ ∀x f.
diff --git a/tests/hol4/betree/betreeMain_TypesTheory.sig b/tests/hol4/betree/betreeMain_TypesTheory.sig
index 5cbe4c6b..a451eae9 100644
--- a/tests/hol4/betree/betreeMain_TypesTheory.sig
+++ b/tests/hol4/betree/betreeMain_TypesTheory.sig
@@ -4,11 +4,29 @@ sig
   
   (*  Definitions  *)
     val betree_be_tree_t_TY_DEF : thm
+    val betree_be_tree_t_betree_be_tree_node_id_cnt : thm
+    val betree_be_tree_t_betree_be_tree_node_id_cnt_fupd : thm
+    val betree_be_tree_t_betree_be_tree_params : thm
+    val betree_be_tree_t_betree_be_tree_params_fupd : thm
+    val betree_be_tree_t_betree_be_tree_root : thm
+    val betree_be_tree_t_betree_be_tree_root_fupd : thm
     val betree_be_tree_t_case_def : thm
     val betree_be_tree_t_size_def : thm
     val betree_internal_t_TY_DEF : thm
+    val betree_internal_t_betree_internal_id : thm
+    val betree_internal_t_betree_internal_id_fupd : thm
+    val betree_internal_t_betree_internal_left : thm
+    val betree_internal_t_betree_internal_left_fupd : thm
+    val betree_internal_t_betree_internal_pivot : thm
+    val betree_internal_t_betree_internal_pivot_fupd : thm
+    val betree_internal_t_betree_internal_right : thm
+    val betree_internal_t_betree_internal_right_fupd : thm
     val betree_internal_t_case_def : thm
     val betree_leaf_t_TY_DEF : thm
+    val betree_leaf_t_betree_leaf_id : thm
+    val betree_leaf_t_betree_leaf_id_fupd : thm
+    val betree_leaf_t_betree_leaf_size : thm
+    val betree_leaf_t_betree_leaf_size_fupd : thm
     val betree_leaf_t_case_def : thm
     val betree_leaf_t_size_def : thm
     val betree_list_t_TY_DEF : thm
@@ -18,41 +36,23 @@ sig
     val betree_message_t_case_def : thm
     val betree_message_t_size_def : thm
     val betree_node_id_counter_t_TY_DEF : thm
+    val betree_node_id_counter_t_betree_node_id_counter_next_node_id : thm
+    val betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd : thm
     val betree_node_id_counter_t_case_def : thm
     val betree_node_id_counter_t_size_def : thm
     val betree_node_t_TY_DEF : thm
     val betree_node_t_case_def : thm
     val betree_node_t_size_def : thm
     val betree_params_t_TY_DEF : thm
+    val betree_params_t_betree_params_min_flush_size : thm
+    val betree_params_t_betree_params_min_flush_size_fupd : thm
+    val betree_params_t_betree_params_split_size : thm
+    val betree_params_t_betree_params_split_size_fupd : thm
     val betree_params_t_case_def : thm
     val betree_params_t_size_def : thm
     val betree_upsert_fun_state_t_TY_DEF : thm
     val betree_upsert_fun_state_t_case_def : thm
     val betree_upsert_fun_state_t_size_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_fupd_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_params_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_params_fupd_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_root_def : thm
-    val recordtype_betree_be_tree_t_seldef_betree_be_tree_root_fupd_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_id_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_id_fupd_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_left_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_left_fupd_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_pivot_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_pivot_fupd_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_right_def : thm
-    val recordtype_betree_internal_t_seldef_betree_internal_right_fupd_def : thm
-    val recordtype_betree_leaf_t_seldef_betree_leaf_id_def : thm
-    val recordtype_betree_leaf_t_seldef_betree_leaf_id_fupd_def : thm
-    val recordtype_betree_leaf_t_seldef_betree_leaf_size_def : thm
-    val recordtype_betree_leaf_t_seldef_betree_leaf_size_fupd_def : thm
-    val recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_def : thm
-    val recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_fupd_def : thm
-    val recordtype_betree_params_t_seldef_betree_params_min_flush_size_def : thm
-    val recordtype_betree_params_t_seldef_betree_params_min_flush_size_fupd_def : thm
-    val recordtype_betree_params_t_seldef_betree_params_split_size_def : thm
-    val recordtype_betree_params_t_seldef_betree_params_split_size_fupd_def : thm
   
   (*  Theorems  *)
     val EXISTS_betree_be_tree_t : thm
@@ -204,6 +204,38 @@ sig
                       $var$('betree_be_tree_t') a0') ⇒
                    $var$('betree_be_tree_t') a0') rep
    
+   [betree_be_tree_t_betree_be_tree_node_id_cnt]  Definition
+      
+      ⊢ ∀b b0 b1.
+          (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0
+   
+   [betree_be_tree_t_betree_be_tree_node_id_cnt_fupd]  Definition
+      
+      ⊢ ∀f b b0 b1.
+          betree_be_tree_t b b0 b1 with
+          betree_be_tree_node_id_cnt updated_by f =
+          betree_be_tree_t b (f b0) b1
+   
+   [betree_be_tree_t_betree_be_tree_params]  Definition
+      
+      ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b
+   
+   [betree_be_tree_t_betree_be_tree_params_fupd]  Definition
+      
+      ⊢ ∀f b b0 b1.
+          betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f =
+          betree_be_tree_t (f b) b0 b1
+   
+   [betree_be_tree_t_betree_be_tree_root]  Definition
+      
+      ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1
+   
+   [betree_be_tree_t_betree_be_tree_root_fupd]  Definition
+      
+      ⊢ ∀f b b0 b1.
+          betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f =
+          betree_be_tree_t b b0 (f b1)
+   
    [betree_be_tree_t_case_def]  Definition
       
       ⊢ ∀a0 a1 a2 f.
@@ -246,6 +278,51 @@ sig
                       $var$('betree_internal_t') a1') ⇒
                    $var$('betree_internal_t') a1') rep
    
+   [betree_internal_t_betree_internal_id]  Definition
+      
+      ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u
+   
+   [betree_internal_t_betree_internal_id_fupd]  Definition
+      
+      ⊢ ∀f u u0 b b0.
+          betree_internal_t u u0 b b0 with betree_internal_id updated_by f =
+          betree_internal_t (f u) u0 b b0
+   
+   [betree_internal_t_betree_internal_left]  Definition
+      
+      ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b
+   
+   [betree_internal_t_betree_internal_left_fupd]  Definition
+      
+      ⊢ ∀f u u0 b b0.
+          betree_internal_t u u0 b b0 with
+          betree_internal_left updated_by f =
+          betree_internal_t u u0 (f b) b0
+   
+   [betree_internal_t_betree_internal_pivot]  Definition
+      
+      ⊢ ∀u u0 b b0.
+          (betree_internal_t u u0 b b0).betree_internal_pivot = u0
+   
+   [betree_internal_t_betree_internal_pivot_fupd]  Definition
+      
+      ⊢ ∀f u u0 b b0.
+          betree_internal_t u u0 b b0 with
+          betree_internal_pivot updated_by f =
+          betree_internal_t u (f u0) b b0
+   
+   [betree_internal_t_betree_internal_right]  Definition
+      
+      ⊢ ∀u u0 b b0.
+          (betree_internal_t u u0 b b0).betree_internal_right = b0
+   
+   [betree_internal_t_betree_internal_right_fupd]  Definition
+      
+      ⊢ ∀f u u0 b b0.
+          betree_internal_t u u0 b b0 with
+          betree_internal_right updated_by f =
+          betree_internal_t u u0 b (f b0)
+   
    [betree_internal_t_case_def]  Definition
       
       ⊢ ∀a0 a1 a2 a3 f.
@@ -267,6 +344,26 @@ sig
                       $var$('betree_leaf_t') a0') ⇒
                    $var$('betree_leaf_t') a0') rep
    
+   [betree_leaf_t_betree_leaf_id]  Definition
+      
+      ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_id = u
+   
+   [betree_leaf_t_betree_leaf_id_fupd]  Definition
+      
+      ⊢ ∀f u u0.
+          betree_leaf_t u u0 with betree_leaf_id updated_by f =
+          betree_leaf_t (f u) u0
+   
+   [betree_leaf_t_betree_leaf_size]  Definition
+      
+      ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0
+   
+   [betree_leaf_t_betree_leaf_size_fupd]  Definition
+      
+      ⊢ ∀f u u0.
+          betree_leaf_t u u0 with betree_leaf_size updated_by f =
+          betree_leaf_t u (f u0)
+   
    [betree_leaf_t_case_def]  Definition
       
       ⊢ ∀a0 a1 f. betree_leaf_t_CASE (betree_leaf_t a0 a1) f = f a0 a1
@@ -355,6 +452,19 @@ sig
                       $var$('betree_node_id_counter_t') a0) ⇒
                    $var$('betree_node_id_counter_t') a0) rep
    
+   [betree_node_id_counter_t_betree_node_id_counter_next_node_id]  Definition
+      
+      ⊢ ∀u. (betree_node_id_counter_t u).
+            betree_node_id_counter_next_node_id =
+            u
+   
+   [betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd]  Definition
+      
+      ⊢ ∀f u.
+          betree_node_id_counter_t u with
+          betree_node_id_counter_next_node_id updated_by f =
+          betree_node_id_counter_t (f u)
+   
    [betree_node_id_counter_t_case_def]  Definition
       
       ⊢ ∀a f.
@@ -424,6 +534,27 @@ sig
                       $var$('betree_params_t') a0') ⇒
                    $var$('betree_params_t') a0') rep
    
+   [betree_params_t_betree_params_min_flush_size]  Definition
+      
+      ⊢ ∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u
+   
+   [betree_params_t_betree_params_min_flush_size_fupd]  Definition
+      
+      ⊢ ∀f u u0.
+          betree_params_t u u0 with
+          betree_params_min_flush_size updated_by f =
+          betree_params_t (f u) u0
+   
+   [betree_params_t_betree_params_split_size]  Definition
+      
+      ⊢ ∀u u0. (betree_params_t u u0).betree_params_split_size = u0
+   
+   [betree_params_t_betree_params_split_size_fupd]  Definition
+      
+      ⊢ ∀f u u0.
+          betree_params_t u u0 with betree_params_split_size updated_by f =
+          betree_params_t u (f u0)
+   
    [betree_params_t_case_def]  Definition
       
       ⊢ ∀a0 a1 f. betree_params_t_CASE (betree_params_t a0 a1) f = f a0 a1
@@ -463,137 +594,6 @@ sig
       ⊢ (∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateAdd a) = 1) ∧
         ∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateSub a) = 1
    
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_def]  Definition
-      
-      ⊢ ∀b b0 b1.
-          (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0
-   
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_fupd_def]  Definition
-      
-      ⊢ ∀f b b0 b1.
-          betree_be_tree_t b b0 b1 with
-          betree_be_tree_node_id_cnt updated_by f =
-          betree_be_tree_t b (f b0) b1
-   
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_params_def]  Definition
-      
-      ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b
-   
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_params_fupd_def]  Definition
-      
-      ⊢ ∀f b b0 b1.
-          betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f =
-          betree_be_tree_t (f b) b0 b1
-   
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_root_def]  Definition
-      
-      ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1
-   
-   [recordtype_betree_be_tree_t_seldef_betree_be_tree_root_fupd_def]  Definition
-      
-      ⊢ ∀f b b0 b1.
-          betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f =
-          betree_be_tree_t b b0 (f b1)
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_id_def]  Definition
-      
-      ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_id_fupd_def]  Definition
-      
-      ⊢ ∀f u u0 b b0.
-          betree_internal_t u u0 b b0 with betree_internal_id updated_by f =
-          betree_internal_t (f u) u0 b b0
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_left_def]  Definition
-      
-      ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_left_fupd_def]  Definition
-      
-      ⊢ ∀f u u0 b b0.
-          betree_internal_t u u0 b b0 with
-          betree_internal_left updated_by f =
-          betree_internal_t u u0 (f b) b0
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_pivot_def]  Definition
-      
-      ⊢ ∀u u0 b b0.
-          (betree_internal_t u u0 b b0).betree_internal_pivot = u0
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_pivot_fupd_def]  Definition
-      
-      ⊢ ∀f u u0 b b0.
-          betree_internal_t u u0 b b0 with
-          betree_internal_pivot updated_by f =
-          betree_internal_t u (f u0) b b0
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_right_def]  Definition
-      
-      ⊢ ∀u u0 b b0.
-          (betree_internal_t u u0 b b0).betree_internal_right = b0
-   
-   [recordtype_betree_internal_t_seldef_betree_internal_right_fupd_def]  Definition
-      
-      ⊢ ∀f u u0 b b0.
-          betree_internal_t u u0 b b0 with
-          betree_internal_right updated_by f =
-          betree_internal_t u u0 b (f b0)
-   
-   [recordtype_betree_leaf_t_seldef_betree_leaf_id_def]  Definition
-      
-      ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_id = u
-   
-   [recordtype_betree_leaf_t_seldef_betree_leaf_id_fupd_def]  Definition
-      
-      ⊢ ∀f u u0.
-          betree_leaf_t u u0 with betree_leaf_id updated_by f =
-          betree_leaf_t (f u) u0
-   
-   [recordtype_betree_leaf_t_seldef_betree_leaf_size_def]  Definition
-      
-      ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0
-   
-   [recordtype_betree_leaf_t_seldef_betree_leaf_size_fupd_def]  Definition
-      
-      ⊢ ∀f u u0.
-          betree_leaf_t u u0 with betree_leaf_size updated_by f =
-          betree_leaf_t u (f u0)
-   
-   [recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_def]  Definition
-      
-      ⊢ ∀u. (betree_node_id_counter_t u).
-            betree_node_id_counter_next_node_id =
-            u
-   
-   [recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_fupd_def]  Definition
-      
-      ⊢ ∀f u.
-          betree_node_id_counter_t u with
-          betree_node_id_counter_next_node_id updated_by f =
-          betree_node_id_counter_t (f u)
-   
-   [recordtype_betree_params_t_seldef_betree_params_min_flush_size_def]  Definition
-      
-      ⊢ ∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u
-   
-   [recordtype_betree_params_t_seldef_betree_params_min_flush_size_fupd_def]  Definition
-      
-      ⊢ ∀f u u0.
-          betree_params_t u u0 with
-          betree_params_min_flush_size updated_by f =
-          betree_params_t (f u) u0
-   
-   [recordtype_betree_params_t_seldef_betree_params_split_size_def]  Definition
-      
-      ⊢ ∀u u0. (betree_params_t u u0).betree_params_split_size = u0
-   
-   [recordtype_betree_params_t_seldef_betree_params_split_size_fupd_def]  Definition
-      
-      ⊢ ∀f u u0.
-          betree_params_t u u0 with betree_params_split_size updated_by f =
-          betree_params_t u (f u0)
-   
    [EXISTS_betree_be_tree_t]  Theorem
       
       ⊢ ∀P. (∃b. P b) ⇔
diff --git a/tests/hol4/hashmap/hashmap_PropertiesScript.sml b/tests/hol4/hashmap/hashmap_PropertiesScript.sml
index c8e87f07..7259f2f5 100644
--- a/tests/hol4/hashmap/hashmap_PropertiesScript.sml
+++ b/tests/hol4/hashmap/hashmap_PropertiesScript.sml
@@ -1040,7 +1040,7 @@ QED
 
 (* TODO: the names introduced by progress are random, which is confusing.
    It also makes the proofs less stable.
-   Try to use the names given by the let-bindings. *)
+   Update the progress tactic to use the names given by the let-bindings. *)
 
 Theorem hash_map_move_elements_loop_fwd_back_spec_aux:
   ∀ hm slots i n.
@@ -1138,16 +1138,17 @@ Proof
     fs [])
   >-(
     (* Prove that index j (update slots i) = index j slots *)
-    pop_assum (qspec_assume ‘int_to_usize j’) >> gvs [] >> massage >> gvs [] >>
+    first_x_assum (qspec_assume ‘int_to_usize j’) >> gvs [] >> massage >> gvs [] >>
     fs [vec_len_def] >>
     massage >> gvs [] >>
     sg ‘j ≠ usize_to_int i’ >- int_tac >> gvs [vec_index_def, vec_update_def] >>
     massage >>
     (* Use the fact that slot_t_lookup k (index i ... slots) = NONE *)
-    last_x_assum (qspec_assume ‘k’) >>
+    first_x_assum (qspec_assume ‘k’) >>
     first_assum sg_premise_tac
     >- (
       sg ‘usize_to_int i < j’ >- int_tac >> fs [] >>
+      sg ‘usize_to_int i ≤ j’ >- int_tac >> fs [] >>
       (* TODO: we have to rewrite key_MEM_j_lookup_i_is_NONE before applying
          metis_tac *)
       assume_tac key_MEM_j_lookup_i_is_NONE >> fs [] >>
@@ -1156,7 +1157,8 @@ Proof
     (* Use the fact that as the key is in the slots after i, it can't be in “hm” (yet) *)
     last_x_assum (qspec_assume ‘j’) >> gvs [] >>
     first_x_assum sg_premise_tac >- (int_tac) >> gvs [] >>
-    first_x_assum imp_res_tac) >>
+    first_x_assum imp_res_tac >>
+    metis_tac []) >>
   (* The conclusion of the theorem (the post-condition) *)
   conj_tac
   >-(
diff --git a/tests/hol4/hashmap/hashmap_TypesTheory.sig b/tests/hol4/hashmap/hashmap_TypesTheory.sig
index 4ad77ac5..a8839fa4 100644
--- a/tests/hol4/hashmap/hashmap_TypesTheory.sig
+++ b/tests/hol4/hashmap/hashmap_TypesTheory.sig
@@ -5,18 +5,18 @@ sig
   (*  Definitions  *)
     val hash_map_t_TY_DEF : thm
     val hash_map_t_case_def : thm
+    val hash_map_t_hash_map_max_load : thm
+    val hash_map_t_hash_map_max_load_factor : thm
+    val hash_map_t_hash_map_max_load_factor_fupd : thm
+    val hash_map_t_hash_map_max_load_fupd : thm
+    val hash_map_t_hash_map_num_entries : thm
+    val hash_map_t_hash_map_num_entries_fupd : thm
+    val hash_map_t_hash_map_slots : thm
+    val hash_map_t_hash_map_slots_fupd : thm
     val hash_map_t_size_def : thm
     val list_t_TY_DEF : thm
     val list_t_case_def : thm
     val list_t_size_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_max_load_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_max_load_factor_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_max_load_factor_fupd_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_max_load_fupd_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_num_entries_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_num_entries_fupd_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_slots_def : thm
-    val recordtype_hash_map_t_seldef_hash_map_slots_fupd_def : thm
   
   (*  Theorems  *)
     val EXISTS_hash_map_t : thm
@@ -72,6 +72,46 @@ sig
       ⊢ ∀a0 a1 a2 a3 f.
           hash_map_t_CASE (hash_map_t a0 a1 a2 a3) f = f a0 a1 a2 a3
    
+   [hash_map_t_hash_map_max_load]  Definition
+      
+      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load = u0
+   
+   [hash_map_t_hash_map_max_load_factor]  Definition
+      
+      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load_factor = p
+   
+   [hash_map_t_hash_map_max_load_factor_fupd]  Definition
+      
+      ⊢ ∀f u p u0 v.
+          hash_map_t u p u0 v with hash_map_max_load_factor updated_by f =
+          hash_map_t u (f p) u0 v
+   
+   [hash_map_t_hash_map_max_load_fupd]  Definition
+      
+      ⊢ ∀f u p u0 v.
+          hash_map_t u p u0 v with hash_map_max_load updated_by f =
+          hash_map_t u p (f u0) v
+   
+   [hash_map_t_hash_map_num_entries]  Definition
+      
+      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_num_entries = u
+   
+   [hash_map_t_hash_map_num_entries_fupd]  Definition
+      
+      ⊢ ∀f u p u0 v.
+          hash_map_t u p u0 v with hash_map_num_entries updated_by f =
+          hash_map_t (f u) p u0 v
+   
+   [hash_map_t_hash_map_slots]  Definition
+      
+      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_slots = v
+   
+   [hash_map_t_hash_map_slots_fupd]  Definition
+      
+      ⊢ ∀f u p u0 v.
+          hash_map_t u p u0 v with hash_map_slots updated_by f =
+          hash_map_t u p u0 (f v)
+   
    [hash_map_t_size_def]  Definition
       
       ⊢ ∀f a0 a1 a2 a3.
@@ -108,46 +148,6 @@ sig
            list_t_size f (ListCons a0 a1 a2) =
            1 + (f a1 + list_t_size f a2)) ∧ ∀f. list_t_size f ListNil = 0
    
-   [recordtype_hash_map_t_seldef_hash_map_max_load_def]  Definition
-      
-      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load = u0
-   
-   [recordtype_hash_map_t_seldef_hash_map_max_load_factor_def]  Definition
-      
-      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load_factor = p
-   
-   [recordtype_hash_map_t_seldef_hash_map_max_load_factor_fupd_def]  Definition
-      
-      ⊢ ∀f u p u0 v.
-          hash_map_t u p u0 v with hash_map_max_load_factor updated_by f =
-          hash_map_t u (f p) u0 v
-   
-   [recordtype_hash_map_t_seldef_hash_map_max_load_fupd_def]  Definition
-      
-      ⊢ ∀f u p u0 v.
-          hash_map_t u p u0 v with hash_map_max_load updated_by f =
-          hash_map_t u p (f u0) v
-   
-   [recordtype_hash_map_t_seldef_hash_map_num_entries_def]  Definition
-      
-      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_num_entries = u
-   
-   [recordtype_hash_map_t_seldef_hash_map_num_entries_fupd_def]  Definition
-      
-      ⊢ ∀f u p u0 v.
-          hash_map_t u p u0 v with hash_map_num_entries updated_by f =
-          hash_map_t (f u) p u0 v
-   
-   [recordtype_hash_map_t_seldef_hash_map_slots_def]  Definition
-      
-      ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_slots = v
-   
-   [recordtype_hash_map_t_seldef_hash_map_slots_fupd_def]  Definition
-      
-      ⊢ ∀f u p u0 v.
-          hash_map_t u p u0 v with hash_map_slots updated_by f =
-          hash_map_t u p u0 (f v)
-   
    [EXISTS_hash_map_t]  Theorem
       
       ⊢ ∀P. (∃h. P h) ⇔
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig b/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig
index bea7eb76..a3e770ea 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig
@@ -5,18 +5,18 @@ sig
   (*  Definitions  *)
     val hashmap_hash_map_t_TY_DEF : thm
     val hashmap_hash_map_t_case_def : thm
+    val hashmap_hash_map_t_hashmap_hash_map_max_load : thm
+    val hashmap_hash_map_t_hashmap_hash_map_max_load_factor : thm
+    val hashmap_hash_map_t_hashmap_hash_map_max_load_factor_fupd : thm
+    val hashmap_hash_map_t_hashmap_hash_map_max_load_fupd : thm
+    val hashmap_hash_map_t_hashmap_hash_map_num_entries : thm
+    val hashmap_hash_map_t_hashmap_hash_map_num_entries_fupd : thm
+    val hashmap_hash_map_t_hashmap_hash_map_slots : thm
+    val hashmap_hash_map_t_hashmap_hash_map_slots_fupd : thm
     val hashmap_hash_map_t_size_def : thm
     val hashmap_list_t_TY_DEF : thm
     val hashmap_list_t_case_def : thm
     val hashmap_list_t_size_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_fupd_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_fupd_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_fupd_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_def : thm
-    val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_fupd_def : thm
   
   (*  Theorems  *)
     val EXISTS_hashmap_hash_map_t : thm
@@ -73,92 +73,92 @@ sig
           hashmap_hash_map_t_CASE (hashmap_hash_map_t a0 a1 a2 a3) f =
           f a0 a1 a2 a3
    
-   [hashmap_hash_map_t_size_def]  Definition
-      
-      ⊢ ∀f a0 a1 a2 a3.
-          hashmap_hash_map_t_size f (hashmap_hash_map_t a0 a1 a2 a3) =
-          1 + pair_size (λv. 0) (λv. 0) a1
-   
-   [hashmap_list_t_TY_DEF]  Definition
-      
-      ⊢ ∃rep.
-          TYPE_DEFINITION
-            (λa0'.
-                 ∀ $var$('hashmap_list_t').
-                   (∀a0'.
-                      (∃a0 a1 a2.
-                         a0' =
-                         (λa0 a1 a2.
-                              ind_type$CONSTR 0 (a0,a1)
-                                (ind_type$FCONS a2 (λn. ind_type$BOTTOM)))
-                           a0 a1 a2 ∧ $var$('hashmap_list_t') a2) ∨
-                      a0' =
-                      ind_type$CONSTR (SUC 0) (ARB,ARB)
-                        (λn. ind_type$BOTTOM) ⇒
-                      $var$('hashmap_list_t') a0') ⇒
-                   $var$('hashmap_list_t') a0') rep
-   
-   [hashmap_list_t_case_def]  Definition
-      
-      ⊢ (∀a0 a1 a2 f v.
-           hashmap_list_t_CASE (HashmapListCons a0 a1 a2) f v = f a0 a1 a2) ∧
-        ∀f v. hashmap_list_t_CASE HashmapListNil f v = v
-   
-   [hashmap_list_t_size_def]  Definition
-      
-      ⊢ (∀f a0 a1 a2.
-           hashmap_list_t_size f (HashmapListCons a0 a1 a2) =
-           1 + (f a1 + hashmap_list_t_size f a2)) ∧
-        ∀f. hashmap_list_t_size f HashmapListNil = 0
-   
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_max_load]  Definition
       
       ⊢ ∀u p u0 v.
           (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load = u0
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_max_load_factor]  Definition
       
       ⊢ ∀u p u0 v.
           (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load_factor =
           p
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_fupd_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_max_load_factor_fupd]  Definition
       
       ⊢ ∀f u p u0 v.
           hashmap_hash_map_t u p u0 v with
           hashmap_hash_map_max_load_factor updated_by f =
           hashmap_hash_map_t u (f p) u0 v
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_fupd_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_max_load_fupd]  Definition
       
       ⊢ ∀f u p u0 v.
           hashmap_hash_map_t u p u0 v with
           hashmap_hash_map_max_load updated_by f =
           hashmap_hash_map_t u p (f u0) v
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_num_entries]  Definition
       
       ⊢ ∀u p u0 v.
           (hashmap_hash_map_t u p u0 v).hashmap_hash_map_num_entries = u
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_fupd_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_num_entries_fupd]  Definition
       
       ⊢ ∀f u p u0 v.
           hashmap_hash_map_t u p u0 v with
           hashmap_hash_map_num_entries updated_by f =
           hashmap_hash_map_t (f u) p u0 v
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_slots]  Definition
       
       ⊢ ∀u p u0 v. (hashmap_hash_map_t u p u0 v).hashmap_hash_map_slots = v
    
-   [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_fupd_def]  Definition
+   [hashmap_hash_map_t_hashmap_hash_map_slots_fupd]  Definition
       
       ⊢ ∀f u p u0 v.
           hashmap_hash_map_t u p u0 v with
           hashmap_hash_map_slots updated_by f =
           hashmap_hash_map_t u p u0 (f v)
    
+   [hashmap_hash_map_t_size_def]  Definition
+      
+      ⊢ ∀f a0 a1 a2 a3.
+          hashmap_hash_map_t_size f (hashmap_hash_map_t a0 a1 a2 a3) =
+          1 + pair_size (λv. 0) (λv. 0) a1
+   
+   [hashmap_list_t_TY_DEF]  Definition
+      
+      ⊢ ∃rep.
+          TYPE_DEFINITION
+            (λa0'.
+                 ∀ $var$('hashmap_list_t').
+                   (∀a0'.
+                      (∃a0 a1 a2.
+                         a0' =
+                         (λa0 a1 a2.
+                              ind_type$CONSTR 0 (a0,a1)
+                                (ind_type$FCONS a2 (λn. ind_type$BOTTOM)))
+                           a0 a1 a2 ∧ $var$('hashmap_list_t') a2) ∨
+                      a0' =
+                      ind_type$CONSTR (SUC 0) (ARB,ARB)
+                        (λn. ind_type$BOTTOM) ⇒
+                      $var$('hashmap_list_t') a0') ⇒
+                   $var$('hashmap_list_t') a0') rep
+   
+   [hashmap_list_t_case_def]  Definition
+      
+      ⊢ (∀a0 a1 a2 f v.
+           hashmap_list_t_CASE (HashmapListCons a0 a1 a2) f v = f a0 a1 a2) ∧
+        ∀f v. hashmap_list_t_CASE HashmapListNil f v = v
+   
+   [hashmap_list_t_size_def]  Definition
+      
+      ⊢ (∀f a0 a1 a2.
+           hashmap_list_t_size f (HashmapListCons a0 a1 a2) =
+           1 + (f a1 + hashmap_list_t_size f a2)) ∧
+        ∀f. hashmap_list_t_size f HashmapListNil = 0
+   
    [EXISTS_hashmap_hash_map_t]  Theorem
       
       ⊢ ∀P. (∃h. P h) ⇔
diff --git a/tests/hol4/misc-constants/constantsTheory.sig b/tests/hol4/misc-constants/constantsTheory.sig
index 6148221f..149d7e22 100644
--- a/tests/hol4/misc-constants/constantsTheory.sig
+++ b/tests/hol4/misc-constants/constantsTheory.sig
@@ -23,6 +23,10 @@ sig
     val p3_c_def : thm
     val pair_t_TY_DEF : thm
     val pair_t_case_def : thm
+    val pair_t_pair_x : thm
+    val pair_t_pair_x_fupd : thm
+    val pair_t_pair_y : thm
+    val pair_t_pair_y_fupd : thm
     val pair_t_size_def : thm
     val q1_body_def : thm
     val q1_c_def : thm
@@ -30,12 +34,6 @@ sig
     val q2_c_def : thm
     val q3_body_def : thm
     val q3_c_def : thm
-    val recordtype_pair_t_seldef_pair_x_def : thm
-    val recordtype_pair_t_seldef_pair_x_fupd_def : thm
-    val recordtype_pair_t_seldef_pair_y_def : thm
-    val recordtype_pair_t_seldef_pair_y_fupd_def : thm
-    val recordtype_wrap_t_seldef_wrap_val_def : thm
-    val recordtype_wrap_t_seldef_wrap_val_fupd_def : thm
     val s1_body_def : thm
     val s1_c_def : thm
     val s2_body_def : thm
@@ -49,6 +47,8 @@ sig
     val wrap_t_TY_DEF : thm
     val wrap_t_case_def : thm
     val wrap_t_size_def : thm
+    val wrap_t_wrap_val : thm
+    val wrap_t_wrap_val_fupd : thm
     val x0_body_def : thm
     val x0_c_def : thm
     val x1_body_def : thm
@@ -198,6 +198,22 @@ sig
       
       ⊢ ∀a0 a1 f. pair_t_CASE (pair_t a0 a1) f = f a0 a1
    
+   [pair_t_pair_x]  Definition
+      
+      ⊢ ∀t t0. (pair_t t t0).pair_x = t
+   
+   [pair_t_pair_x_fupd]  Definition
+      
+      ⊢ ∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0
+   
+   [pair_t_pair_y]  Definition
+      
+      ⊢ ∀t t0. (pair_t t t0).pair_y = t0
+   
+   [pair_t_pair_y_fupd]  Definition
+      
+      ⊢ ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0)
+   
    [pair_t_size_def]  Definition
       
       ⊢ ∀f f1 a0 a1. pair_t_size f f1 (pair_t a0 a1) = 1 + (f a0 + f1 a1)
@@ -226,30 +242,6 @@ sig
       
       ⊢ q3_c = get_return_value q3_body
    
-   [recordtype_pair_t_seldef_pair_x_def]  Definition
-      
-      ⊢ ∀t t0. (pair_t t t0).pair_x = t
-   
-   [recordtype_pair_t_seldef_pair_x_fupd_def]  Definition
-      
-      ⊢ ∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0
-   
-   [recordtype_pair_t_seldef_pair_y_def]  Definition
-      
-      ⊢ ∀t t0. (pair_t t t0).pair_y = t0
-   
-   [recordtype_pair_t_seldef_pair_y_fupd_def]  Definition
-      
-      ⊢ ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0)
-   
-   [recordtype_wrap_t_seldef_wrap_val_def]  Definition
-      
-      ⊢ ∀t. (wrap_t t).wrap_val = t
-   
-   [recordtype_wrap_t_seldef_wrap_val_fupd_def]  Definition
-      
-      ⊢ ∀f t. wrap_t t with wrap_val updated_by f = wrap_t (f t)
-   
    [s1_body_def]  Definition
       
       ⊢ s1_body = Return (int_to_u32 6)
@@ -311,6 +303,14 @@ sig
       
       ⊢ ∀f a. wrap_t_size f (wrap_t a) = 1 + f a
    
+   [wrap_t_wrap_val]  Definition
+      
+      ⊢ ∀t. (wrap_t t).wrap_val = t
+   
+   [wrap_t_wrap_val_fupd]  Definition
+      
+      ⊢ ∀f t. wrap_t t with wrap_val updated_by f = wrap_t (f t)
+   
    [x0_body_def]  Definition
       
       ⊢ x0_body = Return (int_to_u32 0)
diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
index 82c842be..c0ff4e09 100644
--- a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
+++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig
@@ -53,15 +53,11 @@ sig
     val one_t_size_def : thm
     val pair_t_TY_DEF : thm
     val pair_t_case_def : thm
+    val pair_t_pair_x : thm
+    val pair_t_pair_x_fupd : thm
+    val pair_t_pair_y : thm
+    val pair_t_pair_y_fupd : thm
     val pair_t_size_def : thm
-    val recordtype_pair_t_seldef_pair_x_def : thm
-    val recordtype_pair_t_seldef_pair_x_fupd_def : thm
-    val recordtype_pair_t_seldef_pair_y_def : thm
-    val recordtype_pair_t_seldef_pair_y_fupd_def : thm
-    val recordtype_struct_with_pair_t_seldef_struct_with_pair_p_def : thm
-    val recordtype_struct_with_pair_t_seldef_struct_with_pair_p_fupd_def : thm
-    val recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_def : thm
-    val recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_fupd_def : thm
     val refs_test1_fwd_def : thm
     val refs_test2_fwd_def : thm
     val rem_test_fwd_def : thm
@@ -69,9 +65,13 @@ sig
     val struct_with_pair_t_TY_DEF : thm
     val struct_with_pair_t_case_def : thm
     val struct_with_pair_t_size_def : thm
+    val struct_with_pair_t_struct_with_pair_p : thm
+    val struct_with_pair_t_struct_with_pair_p_fupd : thm
     val struct_with_tuple_t_TY_DEF : thm
     val struct_with_tuple_t_case_def : thm
     val struct_with_tuple_t_size_def : thm
+    val struct_with_tuple_t_struct_with_tuple_p : thm
+    val struct_with_tuple_t_struct_with_tuple_p_fupd : thm
     val subs_test_fwd_def : thm
     val sum_t_TY_DEF : thm
     val sum_t_case_def : thm
@@ -577,45 +577,25 @@ sig
       
       ⊢ ∀a0 a1 f. pair_t_CASE (pair_t a0 a1) f = f a0 a1
    
-   [pair_t_size_def]  Definition
-      
-      ⊢ ∀f f1 a0 a1. pair_t_size f f1 (pair_t a0 a1) = 1 + (f a0 + f1 a1)
-   
-   [recordtype_pair_t_seldef_pair_x_def]  Definition
+   [pair_t_pair_x]  Definition
       
       ⊢ ∀t t0. (pair_t t t0).pair_x = t
    
-   [recordtype_pair_t_seldef_pair_x_fupd_def]  Definition
+   [pair_t_pair_x_fupd]  Definition
       
       ⊢ ∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0
    
-   [recordtype_pair_t_seldef_pair_y_def]  Definition
+   [pair_t_pair_y]  Definition
       
       ⊢ ∀t t0. (pair_t t t0).pair_y = t0
    
-   [recordtype_pair_t_seldef_pair_y_fupd_def]  Definition
+   [pair_t_pair_y_fupd]  Definition
       
       ⊢ ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0)
    
-   [recordtype_struct_with_pair_t_seldef_struct_with_pair_p_def]  Definition
-      
-      ⊢ ∀p. (struct_with_pair_t p).struct_with_pair_p = p
-   
-   [recordtype_struct_with_pair_t_seldef_struct_with_pair_p_fupd_def]  Definition
-      
-      ⊢ ∀f p.
-          struct_with_pair_t p with struct_with_pair_p updated_by f =
-          struct_with_pair_t (f p)
-   
-   [recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_def]  Definition
-      
-      ⊢ ∀p. (struct_with_tuple_t p).struct_with_tuple_p = p
-   
-   [recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_fupd_def]  Definition
+   [pair_t_size_def]  Definition
       
-      ⊢ ∀f p.
-          struct_with_tuple_t p with struct_with_tuple_p updated_by f =
-          struct_with_tuple_t (f p)
+      ⊢ ∀f f1 a0 a1. pair_t_size f f1 (pair_t a0 a1) = 1 + (f a0 + f1 a1)
    
    [refs_test1_fwd_def]  Definition
       
@@ -665,6 +645,16 @@ sig
           struct_with_pair_t_size f f1 (struct_with_pair_t a) =
           1 + pair_t_size f f1 a
    
+   [struct_with_pair_t_struct_with_pair_p]  Definition
+      
+      ⊢ ∀p. (struct_with_pair_t p).struct_with_pair_p = p
+   
+   [struct_with_pair_t_struct_with_pair_p_fupd]  Definition
+      
+      ⊢ ∀f p.
+          struct_with_pair_t p with struct_with_pair_p updated_by f =
+          struct_with_pair_t (f p)
+   
    [struct_with_tuple_t_TY_DEF]  Definition
       
       ⊢ ∃rep.
@@ -688,6 +678,16 @@ sig
           struct_with_tuple_t_size f f1 (struct_with_tuple_t a) =
           1 + pair_size f f1 a
    
+   [struct_with_tuple_t_struct_with_tuple_p]  Definition
+      
+      ⊢ ∀p. (struct_with_tuple_t p).struct_with_tuple_p = p
+   
+   [struct_with_tuple_t_struct_with_tuple_p_fupd]  Definition
+      
+      ⊢ ∀f p.
+          struct_with_tuple_t p with struct_with_tuple_p updated_by f =
+          struct_with_tuple_t (f p)
+   
    [subs_test_fwd_def]  Definition
       
       ⊢ ∀x y. subs_test_fwd x y = u32_sub x y