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Proof step 6 from proof fits-law-mod-01 (previous step)

i < 0 ⊦ s2i(sho) = 0, i % s2i(sho) = s2i(i2s(i % s2i(sho))), ¬ i % s2i(sho) < ~32768 ∧ ¬ 32767 < i % s2i(sho)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i % s2i(sho) < ~32768, i < 0, i % s2i(sho) < 0 ⊦ s2i(sho) = 0, i % s2i(sho) = s2i(i2s(i % s2i(sho)))

Rule argument

Additional information

Used simplifier rules: short-max-10: ⊦ 32767 < i → s2i(sho) ≠ i;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ i < 0 ∧ j ≠ 0 → ¬ 0 < i % j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)