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Proof step 11 from proof div-inshort (previous step)

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 cut formula

And obtained the following new goals

Proof step 12:
~ ~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

fma: ~ ~32768 < ~(s2i(sho0) / s2i(sho1))

Additional information

Used simplifier rules: neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: ~ ~32768 < ~(s2i(sho0) / s2i(sho1))