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Diffstat (limited to 'backends/hol4/primitivesArithScript.sml')
| -rw-r--r-- | backends/hol4/primitivesArithScript.sml | 14 |
1 files changed, 14 insertions, 0 deletions
diff --git a/backends/hol4/primitivesArithScript.sml b/backends/hol4/primitivesArithScript.sml index 679ed2cd..727fc8c2 100644 --- a/backends/hol4/primitivesArithScript.sml +++ b/backends/hol4/primitivesArithScript.sml @@ -209,4 +209,18 @@ Proof cooper_tac QED +Theorem pos_mod_pos_lt: + ∀ x y. 0 ≤ x ⇒ 0 < y ⇒ x % y < y +Proof + rw [] >> + qspecl_assume [‘x’, ‘y’] integerTheory.INT_MOD_BOUNDS >> + sg ‘y ≠ 0 ∧ ~(y < 0)’ >- int_tac >> fs [] +QED + +Theorem pos_mod_pos_ineqs: + ∀x y. 0 ≤ x ⇒ 0 < y ⇒ 0 ≤ x % y ∧ x % y < y +Proof + metis_tac [pos_mod_pos_is_pos, pos_mod_pos_lt] +QED + val _ = export_theory () |