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Proof step 16 from proof div-inshort (previous step)

s2i(sho1) ≠ 0, 32768 < ~ s2i(sho0) / s2i(sho1), s2i(sho0) / s2i(sho1) < ~32768, s2i(sho0) / s2i(sho1) < 0, 0 < s2i(sho1), s2i(sho0) < 0 ⊦ s2i(sho1) = 0, s2i(sho1) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-nls seq: ⊦ ¬ i0 < i ∧ 0 ≤ i ∧ 0 < j → ¬ i0 < i / j subst: [j, i, i0] → [s2i(sho1), ~ s2i(sho0), 32768] flags: rewrite

Additional information

Used simplifier rules: short-min-01: ⊦ ¬ s2i(sho) < ~32768;%neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j); from specification int-div%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs Used terms: s2i(sho1), ~ s2i(sho0), 32768