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Proof step 42 from proof div-inshort (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ ¬ i0 < abs(i) ∧ i ≤ 0 ∧ j < 0 → ¬ i0 < i / j
Proof step 44:
¬(¬ 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

Rule argument

spec: int-div inst: name: div-nls-01 seq: ⊦ ¬ i0 < abs(i) ∧ i ≤ 0 ∧ j < 0 → ¬ i0 < i / j subst: [j, i, i0] → [s2i(sho1), ~32768 - s2i(sho1), 32766] flags: rewrite

Additional information

Used terms: s2i(sho1), ~32768 - s2i(sho1), 32766