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Proof step 14 from proof div-inshort (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ j ≠ 0 → ~ i / j = ~(i / j)
Proof step 16:
s2i(sho1) ≠ 0, 32768 < ~ s2i(sho0) / s2i(sho1), s2i(sho0) / s2i(sho1) < ~32768, s2i(sho0) / s2i(sho1) < 0, 0 < s2i(sho1), s2i(sho0) < 0 ⊦ s2i(sho1) = 0, s2i(sho1) = ~1

Rule argument

spec: int-div inst: name: Div-left seq: ⊦ j ≠ 0 → ~ i / j = ~(i / j) subst: [j, i] → [s2i(sho1), s2i(sho0)] flags: rewrite

Additional information

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