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Proof step 45 from proof div-inshort (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ i < j ↔ i + 1 ≤ j
Proof step 47:
s2i(sho0) = ~32768, s2i(sho1) < 0, 32766 < (~32768 - s2i(sho1)) / s2i(sho1), 0 ≤ (~32768 - s2i(sho1)) / s2i(sho1), 0 < (~32768 - s2i(sho1)) / s2i(sho1), 32766 + 1 ≤ abs(~32768 - s2i(sho1)), ~32768 < s2i(sho1) ⊦ s2i(sho1) = 0, s2i(sho1) = ~1, ~32768 = s2i(sho1)

Rule argument

spec: int-abs inst: name: ls-rew-succ seq: ⊦ i < j ↔ i + 1 ≤ j subst: [j, i] → [abs(~32768 - s2i(sho1)), 32766] flags: rewrite

Additional information

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