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Proof step 7 from proof fits-law-mod-01 (previous step)

i % s2i(sho) < ~32768, i < 0, i % s2i(sho) < 0 ⊦ s2i(sho) = 0, i % s2i(sho) = s2i(i2s(i % s2i(sho)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i0 - 1 ≤ ~ abs(j) ∧ j ≠ 0 → ¬ i % j < i0
Proof step 9:
¬(~32768 - 1 ≤ ~ abs(s2i(sho)) ∧ s2i(sho) ≠ 0), i % s2i(sho) < ~32768, i < 0, i % s2i(sho) < 0 ⊦ s2i(sho) = 0, i % s2i(sho) = s2i(i2s(i % s2i(sho)))

Rule argument

seq: ⊦ i0 - 1 ≤ ~ abs(j) ∧ j ≠ 0 → ¬ i % j < i0 subst: [i0, j, i] → [~32768, s2i(sho), i] rotate: F spec: int-div inst: name: mod-nls-04

Additional information

Used terms: ~32768, s2i(sho), i