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Proof step 10 from proof fits-law-mod-01 (previous step)

32769 < abs(s2i(sho)), i % s2i(sho) < 0, i < 0, i % s2i(sho) < ~32768 ⊦ i % s2i(sho) = s2i(i2s(i % s2i(sho))), s2i(sho) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [s2i(sho)] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: short-max-06: ⊦ 32767 ≤ i → ¬ i < s2i(sho);%short-min-02: ⊦ i ≤ ~32768 → ¬ s2i(sho) < i;% ⊦ ¬ j < 0 → abs(j) = j;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ 0 - i = ~ i;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: s2i(sho)