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Proof step 12 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

Rule argument

Additional information

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