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Proof step 39 from proof div-inshort (previous step)

s2i(sho0) = ~32768, 0 < ~32768 / s2i(sho1), s2i(sho1) < 0, 32767 < ~32768 / s2i(sho1) ⊦ s2i(sho1) = 0, s2i(sho1) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
j < 0, i ≤ j ⊦ i / j = (i - j) / j + 1
Proof step 41:
s2i(sho1) < 0 ∧ ~32768 ≤ s2i(sho1), s2i(sho0) = ~32768, 0 < (~32768 - s2i(sho1)) / s2i(sho1) + 1, s2i(sho1) < 0, 32767 < (~32768 - s2i(sho1)) / s2i(sho1) + 1 ⊦ s2i(sho1) = 0, s2i(sho1) = ~1

Rule argument

spec: int-div inst: name: div-rec-01 seq: j < 0, i ≤ j ⊦ i / j = (i - j) / j + 1 subst: [j, i] → [s2i(sho1), ~32768] flags: rewrite

Additional information

Used simplifier rules: short-min-01: ⊦ ¬ s2i(sho) < ~32768;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: s2i(sho1), ~32768