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Proof step 44 from proof div-inshort (previous step)

¬(¬ 32766 < abs(~32768 - s2i(sho1)) ∧ ~32768 - s2i(sho1) ≤ 0 ∧ s2i(sho1) < 0), s2i(sho0) = ~32768, 0 < (~32768 - s2i(sho1)) / s2i(sho1), 0 ≤ (~32768 - s2i(sho1)) / s2i(sho1), 32766 < (~32768 - s2i(sho1)) / s2i(sho1), s2i(sho1) < 0, ~32768 ≤ s2i(sho1) ⊦ s2i(sho1) = ~1, s2i(sho1) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs