diff options
Diffstat (limited to '')
| -rw-r--r-- | backends/hol4/primitivesArithTheory.sig | 10 |
1 files changed, 10 insertions, 0 deletions
diff --git a/backends/hol4/primitivesArithTheory.sig b/backends/hol4/primitivesArithTheory.sig index f7ecccab..531797ac 100644 --- a/backends/hol4/primitivesArithTheory.sig +++ b/backends/hol4/primitivesArithTheory.sig @@ -23,8 +23,10 @@ sig val pos_div_pos_is_pos : thm val pos_div_pos_le : thm val pos_div_pos_le_init : thm + val pos_mod_pos_ineqs : thm val pos_mod_pos_is_pos : thm val pos_mod_pos_le_init : thm + val pos_mod_pos_lt : thm val pos_mul_pos_is_pos : thm val primitivesArith_grammars : type_grammar.grammar * term_grammar.grammar @@ -113,6 +115,10 @@ sig ⊢ ∀x y. 0 ≤ x ⇒ 0 < y ⇒ x / y ≤ x + [pos_mod_pos_ineqs] Theorem + + ⊢ ∀x y. 0 ≤ x ⇒ 0 < y ⇒ 0 ≤ x % y ∧ x % y < y + [pos_mod_pos_is_pos] Theorem ⊢ ∀x y. 0 ≤ x ⇒ 0 < y ⇒ 0 ≤ x % y @@ -121,6 +127,10 @@ sig ⊢ ∀x y. 0 ≤ x ⇒ 0 < y ⇒ x % y ≤ x + [pos_mod_pos_lt] Theorem + + ⊢ ∀x y. 0 ≤ x ⇒ 0 < y ⇒ x % y < y + [pos_mul_pos_is_pos] Theorem ⊢ ∀x y. 0 ≤ x ⇒ 0 ≤ y ⇒ 0 ≤ x * y |