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Proof step 6 from proof div-inshort (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 ≤ i ∧ 0 < j ∨ i < 0 ∧ j < 0 → i / j = abs(i) / abs(j)
Proof step 8:
¬(0 ≤ s2i(sho0) ∧ 0 < s2i(sho1) ∨ s2i(sho0) < 0 ∧ s2i(sho1) < 0), s2i(sho0) / s2i(sho1) < ~32768, s2i(sho0) / s2i(sho1) < 0 ⊦ s2i(sho1) = 0, s2i(sho1) = ~1
Proof step 26:
0 ≤ s2i(sho0) ∧ 0 < s2i(sho1) ∨ s2i(sho0) < 0 ∧ s2i(sho1) < 0, abs(s2i(sho0)) / abs(s2i(sho1)) < ~32768, abs(s2i(sho0)) / abs(s2i(sho1)) < 0 ⊦ s2i(sho1) = 0, s2i(sho1) = ~1

Rule argument

spec: int-div inst: name: abs-intro seq: ⊦ 0 ≤ i ∧ 0 < j ∨ i < 0 ∧ j < 0 → i / j = abs(i) / abs(j) subst: [j, i] → [s2i(sho1), s2i(sho0)] flags: rewrite

Additional information

Used terms: s2i(sho1), s2i(sho0)