Merge branch 'main' into son_traits and fix some issues

11 files changed, 348 insertions, 83 deletions

diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index 531ec94f..3359ecdb 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -211,9 +211,11 @@ def intTacPreprocess (extraPreprocess :  Tactic.TacticM Unit) : Tactic.TacticM U
   let _ ← introHasIntPropInstances
   -- Extra preprocessing, before we split on the disjunctions
   extraPreprocess
-  -- Split
-  let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
-  splitOnAsms asms.toList
+  -- Split - note that the extra-preprocessing step might actually have
+  -- proven the goal (by doing simplifications for instance)
+  Tactic.allGoals do
+    let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
+    splitOnAsms asms.toList
 
 elab "int_tac_preprocess" : tactic =>
   intTacPreprocess (do pure ())
@@ -238,7 +240,7 @@ def intTac (splitGoalConjs : Bool) (extraPreprocess :  Tactic.TacticM Unit) : Ta
   -- the goal. I think before leads to a smaller proof term?
   Tactic.allGoals (intTacPreprocess extraPreprocess)
   -- More preprocessing
-  Tactic.allGoals (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard)
+  Tactic.allGoals (Utils.tryTac (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard))
   -- Split the conjunctions in the goal
   if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
   -- Call linarith
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index db672489..47751c8a 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -16,14 +16,15 @@ def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
    add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
-   -- Reveal the concrete bounds
+   -- Reveal the concrete bounds, simplify calls to [ofInt]
    Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
                  ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
                  ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
                  ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
                  ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
                  ``Usize.min
-                 ] [] [] .wildcard
+                 ] [``Scalar.ofInt_val_eq, ``Scalar.neq_to_neq_val] [] .wildcard
+   
 
 elab "scalar_tac_preprocess" : tactic =>
   intTacPreprocess scalarTacExtraPreprocess
@@ -50,4 +51,16 @@ example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
 example (x : U32 × U32) : 0 ≤ x.fst.val := by
   scalar_tac
 
+-- Checking that we properly handle [ofInt]
+example : U32.ofInt 1 ≤ U32.max := by
+  scalar_tac
+
+example (x : Int) (h0 : 0 ≤ x) (h1 : x ≤ U32.max) :
+  U32.ofInt x (by constructor <;> scalar_tac) ≤ U32.max := by
+  scalar_tac
+
+-- Not equal
+example (x : U32) (h0 : ¬ x = U32.ofInt 0) : 0 < x.val := by
+  scalar_tac
+
 end Arith
diff --git a/backends/lean/Base/Diverge/Base.lean b/backends/lean/Base/Diverge/Base.lean
index 1d548389..6a52387d 100644
--- a/backends/lean/Base/Diverge/Base.lean
+++ b/backends/lean/Base/Diverge/Base.lean
@@ -270,7 +270,7 @@ namespace Fix
     simp [karrow_rel, result_rel]
     have hg := hg Hrgh; simp [result_rel] at hg
     cases heq0: g fg <;> simp_all
-    rename_i y _
+    rename_i _ y
     have hh := hh y Hrgh; simp [result_rel] at hh
     simp_all
 
@@ -546,7 +546,7 @@ namespace FixI
   termination_by for_all_fin_aux n _ m h => n - m
   decreasing_by
     simp_wf
-    apply Nat.sub_add_lt_sub <;> simp
+    apply Nat.sub_add_lt_sub <;> try simp
     simp_all [Arith.add_one_le_iff_le_ne]
 
   def for_all_fin {n : Nat} (f : Fin n → Prop) := for_all_fin_aux f 0 (by simp)
@@ -569,7 +569,6 @@ namespace FixI
       intro i h3; cases i; simp_all
       linarith
     case succ k hi =>
-      simp_all
       intro m hk hmn
       intro hf i hmi
       have hne: m ≠ n := by
@@ -580,7 +579,6 @@ namespace FixI
         -- Yes: simply use the `for_all_fin_aux` hyp
         unfold for_all_fin_aux at hf
         simp_all
-        tauto
       else
         -- No: use the induction hypothesis
         have hlt: m < i := by simp_all [Nat.lt_iff_le_and_ne]
@@ -726,8 +724,8 @@ namespace Ex1
   theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
     intro k x
     simp [list_nth_body]
-    split <;> simp
-    split <;> simp
+    split <;> try simp
+    split <;> try simp
 
   def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
 
@@ -767,8 +765,8 @@ namespace Ex2
   theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
     intro k x
     simp [list_nth_body]
-    split <;> simp
-    split <;> simp
+    split <;> try simp
+    split <;> try simp
     apply is_valid_p_bind <;> intros <;> simp_all
 
   def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
@@ -845,7 +843,7 @@ namespace Ex3
     ∀ k x, is_valid_p k (λ k => is_even_is_odd_body k x) := by
     intro k x
     simp [is_even_is_odd_body]
-    split <;> simp <;> split <;> simp
+    split <;> (try simp) <;> split <;> try simp
     apply is_valid_p_bind; simp
     intros; split <;> simp
     apply is_valid_p_bind; simp
@@ -878,7 +876,7 @@ namespace Ex3
     -- inductives on the fly).
     -- The simplest is to repeatedly split then simplify (we identify
     -- the outer match or monadic let-binding, and split on its scrutinee)
-    split <;> simp
+    split <;> try simp
     cases H0 : fix is_even_is_odd_body (Sum.inr (i - 1)) <;> simp
     rename_i v
     split <;> simp
@@ -891,7 +889,7 @@ namespace Ex3
     simp [is_even, is_odd]
     conv => lhs; rw [Heq]; simp; rw [is_even_is_odd_body]; simp
     -- Same remark as for `even`
-    split <;> simp
+    split <;> try simp
     cases H0 : fix is_even_is_odd_body (Sum.inl (i - 1)) <;> simp
     rename_i v
     split <;> simp
@@ -938,7 +936,7 @@ namespace Ex4
     intro k
     apply (Funs.is_valid_p_is_valid_p tys)
     simp [Funs.is_valid_p]
-    (repeat (apply And.intro)) <;> intro x <;> simp at x <;>
+    (repeat (apply And.intro)) <;> intro x <;> (try simp at x) <;>
     simp only [is_even_body, is_odd_body]
     -- Prove the validity of the individual bodies
     . split <;> simp
@@ -995,9 +993,9 @@ namespace Ex5
     (ls : List a) :
     is_valid_p k (λ k => map (f k) ls) := by
     induction ls <;> simp [map]
-    apply is_valid_p_bind <;> simp_all
+    apply is_valid_p_bind <;> try simp_all
     intros
-    apply is_valid_p_bind <;> simp_all
+    apply is_valid_p_bind <;> try simp_all
 
   /- An example which uses map -/
   inductive Tree (a : Type) :=
@@ -1016,8 +1014,8 @@ namespace Ex5
     ∀ k x, is_valid_p k (λ k => @id_body a k x) := by
     intro k x
     simp only [id_body]
-    split <;> simp
-    apply is_valid_p_bind <;> simp [*]
+    split <;> try simp
+    apply is_valid_p_bind <;> try simp [*]
     -- We have to show that `map k tl` is valid
     apply map_is_valid;
     -- Remark: if we don't do the intro, then the last step is expensive:
@@ -1077,12 +1075,11 @@ namespace Ex6
     intro k
     apply (Funs.is_valid_p_is_valid_p tys)
     simp [Funs.is_valid_p]
-    (repeat (apply And.intro)); intro x; simp at x
+    (repeat (apply And.intro)); intro x; try simp at x
     simp only [list_nth_body]
     -- Prove the validity of the individual bodies
     intro k x
-    simp [list_nth_body]
-    split <;> simp
+    split <;> try simp
     split <;> simp
 
   -- Writing the proof terms explicitly
diff --git a/backends/lean/Base/Diverge/Elab.lean b/backends/lean/Base/Diverge/Elab.lean
index f109e847..c6628486 100644
--- a/backends/lean/Base/Diverge/Elab.lean
+++ b/backends/lean/Base/Diverge/Elab.lean
@@ -1089,7 +1089,7 @@ namespace Tests
       intro i hpos h
       -- We can directly use `rw [list_nth]`!
       rw [list_nth]; simp
-      split <;> simp [*]
+      split <;> try simp [*]
       . tauto
       . -- TODO: we shouldn't have to do that
         have hneq : 0 < i := by cases i <;> rename_i a _ <;> simp_all; cases a <;> simp_all
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean
index f10ec4e7..79de93d5 100644
--- a/backends/lean/Base/IList/IList.lean
+++ b/backends/lean/Base/IList/IList.lean
@@ -294,7 +294,6 @@ open Arith in
     have := tl.len_pos
     linarith
   else
-    simp at hineq
     have : 0 < i := by int_tac
     simp [*]
     apply hi
@@ -419,8 +418,8 @@ theorem index_itake_append_end [Inhabited α] (i j : Int) (l0 l1 : List α)
   match l0 with
   | [] => by
     simp at *
-    have := index_itake i j l1 (by simp_all) (by simp_all) (by simp_all; int_tac)
-    simp [*]
+    have := index_itake i j l1 (by simp_all) (by simp_all) (by int_tac)
+    try simp [*]
   | hd :: tl =>
     have : ¬ i = 0 := by simp at *; int_tac
     if hj : j = 0 then by simp_all; int_tac -- Contradiction
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 9e65d3c0..ec9665a5 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -533,6 +533,36 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
   apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
 
+@[cepspec] theorem Isize.add_spec {x y : Isize}
+  (hmin : Isize.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ Isize.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
+@[cepspec] theorem I8.add_spec {x y : I8}
+  (hmin : I8.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I8.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
+@[cepspec] theorem I16.add_spec {x y : I16}
+  (hmin : I16.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I16.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
+@[cepspec] theorem I32.add_spec {x y : I32}
+  (hmin : I32.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I32.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
+@[cepspec] theorem I64.add_spec {x y : I64}
+  (hmin : I64.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I64.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
+@[cepspec] theorem I128.add_spec {x y : I128}
+  (hmin : I128.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I128.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val :=
+  Scalar.add_spec hmin hmax
+
 -- Generic theorem - shouldn't be used much
 @[cpspec]
 theorem Scalar.sub_spec {ty} {x y : Scalar ty}
@@ -582,6 +612,36 @@ theorem Scalar.sub_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
   apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
 
+@[cepspec] theorem Isize.sub_spec {x y : Isize} (hmin : Isize.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ Isize.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
+@[cepspec] theorem I8.sub_spec {x y : I8} (hmin : I8.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ I8.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
+@[cepspec] theorem I16.sub_spec {x y : I16} (hmin : I16.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ I16.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
+@[cepspec] theorem I32.sub_spec {x y : I32} (hmin : I32.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ I32.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
+@[cepspec] theorem I64.sub_spec {x y : I64} (hmin : I64.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ I64.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
+@[cepspec] theorem I128.sub_spec {x y : I128} (hmin : I128.min ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ I128.max) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val :=
+  Scalar.sub_spec hmin hmax
+
 -- Generic theorem - shouldn't be used much
 theorem Scalar.mul_spec {ty} {x y : Scalar ty}
   (hmin : Scalar.min ty ≤ x.val * y.val)
@@ -628,6 +688,36 @@ theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
   apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
 
+@[cepspec] theorem Isize.mul_spec {x y : Isize} (hmin : Isize.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ Isize.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
+@[cepspec] theorem I8.mul_spec {x y : I8} (hmin : I8.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ I8.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
+@[cepspec] theorem I16.mul_spec {x y : I16} (hmin : I16.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ I16.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
+@[cepspec] theorem I32.mul_spec {x y : I32} (hmin : I32.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ I32.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
+@[cepspec] theorem I64.mul_spec {x y : I64} (hmin : I64.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ I64.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
+@[cepspec] theorem I128.mul_spec {x y : I128} (hmin : I128.min ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ I128.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val :=
+  Scalar.mul_spec hmin hmax
+
 -- Generic theorem - shouldn't be used much
 @[cpspec]
 theorem Scalar.div_spec {ty} {x y : Scalar ty}
@@ -681,6 +771,48 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
   ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
   apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
 
+@[cepspec] theorem Isize.div_spec (x : Isize) {y : Isize}
+  (hnz : y.val ≠ 0)
+  (hmin : Isize.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ Isize.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
+@[cepspec] theorem I8.div_spec (x : I8) {y : I8}
+  (hnz : y.val ≠ 0)
+  (hmin : I8.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ I8.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
+@[cepspec] theorem I16.div_spec (x : I16) {y : I16}
+  (hnz : y.val ≠ 0)
+  (hmin : I16.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ I16.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
+@[cepspec] theorem I32.div_spec (x : I32) {y : I32}
+  (hnz : y.val ≠ 0)
+  (hmin : I32.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ I32.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
+@[cepspec] theorem I64.div_spec (x : I64) {y : I64}
+  (hnz : y.val ≠ 0)
+  (hmin : I64.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ I64.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
+@[cepspec] theorem I128.div_spec (x : I128) {y : I128}
+  (hnz : y.val ≠ 0)
+  (hmin : I128.min ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ I128.max):
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val :=
+  Scalar.div_spec hnz hmin hmax
+
 -- Generic theorem - shouldn't be used much
 @[cpspec]
 theorem Scalar.rem_spec {ty} {x y : Scalar ty}
@@ -734,6 +866,41 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
   ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
   apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
 
+@[cepspec] theorem I8.rem_spec (x : I8) {y : I8}
+  (hnz : y.val ≠ 0)
+  (hmin : I8.min ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ I8.max):
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val :=
+  Scalar.rem_spec hnz hmin hmax
+
+@[cepspec] theorem I16.rem_spec (x : I16) {y : I16}
+  (hnz : y.val ≠ 0)
+  (hmin : I16.min ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ I16.max):
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val :=
+  Scalar.rem_spec hnz hmin hmax
+
+@[cepspec] theorem I32.rem_spec (x : I32) {y : I32}
+  (hnz : y.val ≠ 0)
+  (hmin : I32.min ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ I32.max):
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val :=
+  Scalar.rem_spec hnz hmin hmax
+
+@[cepspec] theorem I64.rem_spec (x : I64) {y : I64}
+  (hnz : y.val ≠ 0)
+  (hmin : I64.min ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ I64.max):
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val :=
+  Scalar.rem_spec hnz hmin hmax
+
+@[cepspec] theorem I128.rem_spec (x : I128) {y : I128}
+  (hnz : y.val ≠ 0)
+  (hmin : I128.min ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ I128.max):
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val :=
+  Scalar.rem_spec hnz hmin hmax
+
 -- ofIntCore
 -- TODO: typeclass?
 def Isize.ofIntCore := @Scalar.ofIntCore .Isize
@@ -751,33 +918,34 @@ def U128.ofIntCore  := @Scalar.ofIntCore .U128
 
 --  ofInt
 -- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
-postfix:74  "%isize" => Isize.ofInt
-postfix:74  "%i8"    => I8.ofInt
-postfix:74  "%i16"   => I16.ofInt
-postfix:74  "%i32"   => I32.ofInt
-postfix:74  "%i64"   => I64.ofInt
-postfix:74  "%i128"  => I128.ofInt
-postfix:74  "%usize" => Usize.ofInt
-postfix:74  "%u8"    => U8.ofInt
-postfix:74  "%u16"   => U16.ofInt
-postfix:74  "%u32"   => U32.ofInt
-postfix:74  "%u64"   => U64.ofInt
-postfix:74  "%u128"  => U128.ofInt
-
-example : Result U32 := 1%u32 + 2%u32
+abbrev Isize.ofInt := @Scalar.ofInt .Isize
+abbrev I8.ofInt    := @Scalar.ofInt .I8
+abbrev I16.ofInt   := @Scalar.ofInt .I16
+abbrev I32.ofInt   := @Scalar.ofInt .I32
+abbrev I64.ofInt   := @Scalar.ofInt .I64
+abbrev I128.ofInt  := @Scalar.ofInt .I128
+abbrev Usize.ofInt := @Scalar.ofInt .Usize
+abbrev U8.ofInt    := @Scalar.ofInt .U8
+abbrev U16.ofInt   := @Scalar.ofInt .U16
+abbrev U32.ofInt   := @Scalar.ofInt .U32
+abbrev U64.ofInt   := @Scalar.ofInt .U64
+abbrev U128.ofInt  := @Scalar.ofInt .U128
+
+postfix:max "#isize" => Isize.ofInt
+postfix:max "#i8"    => I8.ofInt
+postfix:max "#i16"   => I16.ofInt
+postfix:max "#i32"   => I32.ofInt
+postfix:max "#i64"   => I64.ofInt
+postfix:max "#i128"  => I128.ofInt
+postfix:max "#usize" => Usize.ofInt
+postfix:max "#u8"    => U8.ofInt
+postfix:max "#u16"   => U16.ofInt
+postfix:max "#u32"   => U32.ofInt
+postfix:max "#u64"   => U64.ofInt
+postfix:max "#u128"  => U128.ofInt
+
+-- Testing the notations
+example : Result Usize := 0#usize + 1#usize
 
 -- TODO: factor those lemmas out
 @[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
@@ -819,7 +987,6 @@ example : Result U32 := 1%u32 + 2%u32
 @[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by
   apply Scalar.ofInt_val_eq h
 
-
 -- Comparisons
 instance {ty} : LT (Scalar ty) where
   lt a b := LT.lt a.val b.val
@@ -847,6 +1014,9 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
 instance (ty : ScalarTy) : CoeOut (Scalar ty) Int where
   coe := λ v => v.val
 
+@[simp] theorem Scalar.neq_to_neq_val {ty} : ∀ {i j : Scalar ty}, (¬ i = j) ↔ ¬ i.val = j.val := by
+  intro i j; cases i; cases j; simp
+
 -- -- We now define a type class that subsumes the various machine integer types, so
 -- -- as to write a concise definition for scalar_cast, rather than exhaustively
 -- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
diff --git a/backends/lean/Base/Progress/Base.lean b/backends/lean/Base/Progress/Base.lean
index 6f820a84..76a92795 100644
--- a/backends/lean/Base/Progress/Base.lean
+++ b/backends/lean/Base/Progress/Base.lean
@@ -167,7 +167,8 @@ structure PSpecClassExprAttr where
   deriving Inhabited
 
 -- TODO: the original function doesn't define correctly the `addImportedFn`. Do a PR?
-def mkMapDeclarationExtension [Inhabited α] (name : Name := by exact decl_name%) : IO (MapDeclarationExtension α) :=
+def mkMapDeclarationExtension [Inhabited α] (name : Name := by exact decl_name%) :
+  IO (MapDeclarationExtension α) :=
   registerSimplePersistentEnvExtension {
     name          := name,
     addImportedFn := fun a => a.foldl (fun s a => a.foldl (fun s (k, v) => s.insert k v) s) RBMap.empty,
@@ -175,6 +176,54 @@ def mkMapDeclarationExtension [Inhabited α] (name : Name := by exact decl_name%
     toArrayFn     := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
   }
 
+-- Declare an extension of maps of maps (using [RBMap]).
+-- The important point is that we need to merge the bound values (which are maps).
+def mkMapMapDeclarationExtension [Inhabited β] (ord : α → α → Ordering)
+  (name : Name := by exact decl_name%) :
+  IO (MapDeclarationExtension (RBMap α β ord)) :=
+  registerSimplePersistentEnvExtension {
+    name          := name,
+    addImportedFn := fun a =>
+      a.foldl (fun s a => a.foldl (
+        -- We need to merge the maps
+        fun s (k0, k1_to_v) =>
+        match s.find? k0 with
+        | none =>
+          -- No binding: insert one
+          s.insert k0 k1_to_v
+        | some m =>
+          -- There is already a binding: merge
+          let m := RBMap.fold (fun m k v => m.insert k v) m k1_to_v
+          s.insert k0 m)
+          s) RBMap.empty,
+    addEntryFn    := fun s n => s.insert n.1 n.2 ,
+    toArrayFn     := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
+  }
+
+-- Declare an extension of maps of maps (using [HashMap]).
+-- The important point is that we need to merge the bound values (which are maps).
+def mkMapHashMapDeclarationExtension [BEq α] [Hashable α] [Inhabited β]
+  (name : Name := by exact decl_name%) :
+  IO (MapDeclarationExtension (HashMap α β)) :=
+  registerSimplePersistentEnvExtension {
+    name          := name,
+    addImportedFn := fun a =>
+      a.foldl (fun s a => a.foldl (
+        -- We need to merge the maps
+        fun s (k0, k1_to_v) =>
+        match s.find? k0 with
+        | none =>
+          -- No binding: insert one
+          s.insert k0 k1_to_v
+        | some m =>
+          -- There is already a binding: merge
+          let m := HashMap.fold (fun m k v => m.insert k v) m k1_to_v
+          s.insert k0 m)
+          s) RBMap.empty,
+    addEntryFn    := fun s n => s.insert n.1 n.2 ,
+    toArrayFn     := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
+  }
+
 /- The persistent map from function to pspec theorems. -/
 initialize pspecAttr : PSpecAttr ← do
   let ext ← mkMapDeclarationExtension `pspecMap
@@ -200,7 +249,8 @@ initialize pspecAttr : PSpecAttr ← do
 
 /- The persistent map from type classes to pspec theorems -/
 initialize pspecClassAttr : PSpecClassAttr ← do
-  let ext : MapDeclarationExtension (NameMap Name) ← mkMapDeclarationExtension `pspecClassMap
+  let ext : MapDeclarationExtension (NameMap Name) ←
+    mkMapMapDeclarationExtension Name.quickCmp `pspecClassMap
   let attrImpl : AttributeImpl  := {
     name := `cpspec
     descr := "Marks theorems to use for type classes with the `progress` tactic"
@@ -231,7 +281,8 @@ initialize pspecClassAttr : PSpecClassAttr ← do
 
 /- The 2nd persistent map from type classes to pspec theorems -/
 initialize pspecClassExprAttr : PSpecClassExprAttr ← do
-  let ext : MapDeclarationExtension (HashMap Expr Name) ← mkMapDeclarationExtension `pspecClassExprMap
+  let ext : MapDeclarationExtension (HashMap Expr Name) ←
+    mkMapHashMapDeclarationExtension `pspecClassExprMap
   let attrImpl : AttributeImpl  := {
     name := `cepspec
     descr := "Marks theorems to use for type classes with the `progress` tactic"
diff --git a/backends/lean/Base/Progress/Progress.lean b/backends/lean/Base/Progress/Progress.lean
index 6a4729dc..8b0759c5 100644
--- a/backends/lean/Base/Progress/Progress.lean
+++ b/backends/lean/Base/Progress/Progress.lean
@@ -110,8 +110,9 @@ def progressWith (fExpr : Expr) (th : TheoremOrLocal)
     -- then continue splitting the post-condition
     splitEqAndPost fun hEq hPost ids => do
     trace[Progress] "eq and post:\n{hEq} : {← inferType hEq}\n{hPost}"
-    simpAt [] [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
-           [hEq.fvarId!] (.targets #[] true)
+    tryTac (
+      simpAt [] [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
+             [hEq.fvarId!] (.targets #[] true))
     -- Clear the equality, unless the user requests not to do so
     let mgoal ← do
       if keep.isSome then getMainGoal
@@ -242,21 +243,26 @@ def progressAsmsOrLookupTheorem (keep : Option Name) (withTh : Option TheoremOrL
     tryLookupApply keep ids splitPost asmTac fExpr "pspec theorem" pspec do
     -- It failed: try to lookup a *class* expr spec theorem (those are more
     -- specific than class spec theorems)
+    trace[Progress] "Failed using a pspec theorem: trying to lookup a pspec class expr theorem"
     let pspecClassExpr ← do
       match getFirstArg args with
       | none => pure none
       | some arg => do
+        trace[Progress] "Using: f:{fName}, arg: {arg}"
         let thName ← pspecClassExprAttr.find? fName arg
         pure (thName.map fun th => .Theorem th)
     tryLookupApply keep ids splitPost asmTac fExpr "pspec class expr theorem" pspecClassExpr do
     -- It failed: try to lookup a *class* spec theorem
+    trace[Progress] "Failed using a pspec class expr theorem: trying to lookup a pspec class theorem"
     let pspecClass ← do
       match ← getFirstArgAppName args with
       | none => pure none
       | some argName => do
+        trace[Progress] "Using: f: {fName}, arg: {argName}"
         let thName ← pspecClassAttr.find? fName argName
         pure (thName.map fun th => .Theorem th)
     tryLookupApply keep ids splitPost asmTac fExpr "pspec class theorem" pspecClass do
+    trace[Progress] "Failed using a pspec class theorem: trying to use a recursive assumption"
     -- Try a recursive call - we try the assumptions of kind "auxDecl"
     let ctx ← Lean.MonadLCtx.getLCtx
     let decls ← ctx.getAllDecls
@@ -314,12 +320,14 @@ def evalProgress (args : TSyntax `Progress.progressArgs) : TacticM Unit := do
     else pure none
   let ids :=
     let args := asArgs.getArgs
-    let args := (args.get! 2).getSepArgs
-    args.map (λ s => if s.isIdent then some s.getId else none)
+    if args.size > 2 then
+      let args := (args.get! 2).getSepArgs
+      args.map (λ s => if s.isIdent then some s.getId else none)
+    else #[]
   trace[Progress] "User-provided ids: {ids}"
   let splitPost : Bool :=
     let args := asArgs.getArgs
-    (args.get! 3).getArgs.size > 0
+    args.size > 3 ∧ (args.get! 3).getArgs.size > 0
   trace[Progress] "Split post: {splitPost}"
   /- For scalarTac we have a fast track: if the goal is not a linear
      arithmetic goal, we skip (note that otherwise, scalarTac would try
@@ -343,11 +351,14 @@ elab "progress" args:progressArgs : tactic =>
 namespace Test
   open Primitives Result
 
-  set_option trace.Progress true
-  set_option pp.rawOnError true
+  -- Show the traces
+  -- set_option trace.Progress true
+  -- set_option pp.rawOnError true
 
-  #eval showStoredPSpec
-  #eval showStoredPSpecClass
+  -- The following commands display the databases of theorems
+  -- #eval showStoredPSpec
+  -- #eval showStoredPSpecClass
+  -- #eval showStoredPSpecExprClass
 
   example {ty} {x y : Scalar ty}
     (hmin : Scalar.min ty ≤ x.val + y.val)
@@ -363,6 +374,12 @@ namespace Test
     progress keep h with Scalar.add_spec as ⟨ z ⟩
     simp [*, h]
 
+  example {x y : U32}
+    (hmax : x.val + y.val ≤ U32.max) :
+    ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+    progress keep _ as ⟨ z, h1 .. ⟩
+    simp [*, h1]
+
   /- Checking that universe instantiation works: the original spec uses
      `α : Type u` where u is quantified, while here we use `α : Type 0` -/
   example {α : Type} (v: Vec α) (i: Usize) (x : α)
diff --git a/backends/lean/Base/Utils.lean b/backends/lean/Base/Utils.lean
index 1f8f1455..5224e1c3 100644
--- a/backends/lean/Base/Utils.lean
+++ b/backends/lean/Base/Utils.lean
@@ -301,6 +301,10 @@ example : Nat := by
 example (x : Bool) : Nat := by
   cases x <;> custom_let x := 3 <;> apply x
 
+-- Attempt to apply a tactic
+def tryTac (tac : TacticM Unit) : TacticM Unit := do
+  let _ ← tryTactic tac
+
 -- Repeatedly apply a tactic
 partial def repeatTac (tac : TacticM Unit) : TacticM Unit := do
   try
diff --git a/backends/lean/lake-manifest.json b/backends/lean/lake-manifest.json
index 5a089838..934ee2d9 100644
--- a/backends/lean/lake-manifest.json
+++ b/backends/lean/lake-manifest.json
@@ -1,39 +1,51 @@
-{"version": 4,
+{"version": 5,
  "packagesDir": "lake-packages",
  "packages":
  [{"git":
    {"url": "https://github.com/EdAyers/ProofWidgets4",
     "subDir?": null,
-    "rev": "c43db94a8f495dad37829e9d7ad65483d68c86b8",
+    "rev": "a0c2cd0ac3245a0dade4f925bcfa97e06dd84229",
+    "opts": {},
     "name": "proofwidgets",
-    "inputRev?": "v0.0.11"}},
+    "inputRev?": "v0.0.13",
+    "inherited": true}},
   {"git":
    {"url": "https://github.com/mhuisi/lean4-cli.git",
     "subDir?": null,
-    "rev": "5a858c32963b6b19be0d477a30a1f4b6c120be7e",
+    "rev": "21dac2e9cc7e3cf7da5800814787b833e680b2fd",
+    "opts": {},
     "name": "Cli",
-    "inputRev?": "nightly"}},
+    "inputRev?": "nightly",
+    "inherited": true}},
   {"git":
    {"url": "https://github.com/leanprover-community/mathlib4.git",
     "subDir?": null,
-    "rev": "fa05951a270fef2873666c46f138e90338cd48d6",
+    "rev": "226948a52f8e19ad95ff6025a96784d7e7ed6ed0",
+    "opts": {},
     "name": "mathlib",
-    "inputRev?": null}},
+    "inputRev?": null,
+    "inherited": false}},
   {"git":
    {"url": "https://github.com/gebner/quote4",
     "subDir?": null,
-    "rev": "c0d9516f44d07feee01c1103c8f2f7c24a822b55",
+    "rev": "e75daed95ad1c92af4e577fea95e234d7a8401c1",
+    "opts": {},
     "name": "Qq",
-    "inputRev?": "master"}},
+    "inputRev?": "master",
+    "inherited": true}},
   {"git":
    {"url": "https://github.com/JLimperg/aesop",
     "subDir?": null,
-    "rev": "f04538ab6ad07642368cf11d2702acc0a9b4bcee",
+    "rev": "1a0cded2be292b5496e659b730d2accc742de098",
+    "opts": {},
     "name": "aesop",
-    "inputRev?": "master"}},
+    "inputRev?": "master",
+    "inherited": true}},
   {"git":
    {"url": "https://github.com/leanprover/std4",
     "subDir?": null,
-    "rev": "dff883c55395438ae2a5c65ad5ddba084b600feb",
+    "rev": "ba5e5e3af519b4fc5221ad0fa4b2c87276f1d323",
+    "opts": {},
     "name": "std",
-    "inputRev?": "main"}}]}
+    "inputRev?": "main",
+    "inherited": true}}]}
diff --git a/backends/lean/lean-toolchain b/backends/lean/lean-toolchain
index 334c5053..fbca4d37 100644
--- a/backends/lean/lean-toolchain
+++ b/backends/lean/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:nightly-2023-07-12
\ No newline at end of file
+leanprover/lean4:v4.0.0
\ No newline at end of file