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Proof step 18 from proof mod-inshort (previous step)

0 ≤ s2i(sho0), s2i(sho1) < 0, 32767 < s2i(sho0) % s2i(sho1), 0 < s2i(sho0) % s2i(sho1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mod-nls-03 seq: ⊦ i ≤ i0 ∧ 0 ≤ i0 ∧ j ≠ 0 → ¬ i0 < i % j subst: [j, i, i0] → [s2i(sho1), s2i(sho0), 32767] flags: rewrite

Additional information

Used simplifier rules: short-ngr: ⊦ ¬ 32767 < s2i(sho);%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs Used terms: s2i(sho1), s2i(sho0), 32767