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Proof step 7 from proof short-mod (previous step)

~32768 ≤ s2i(sho), s2i(sho) ≤ 32767, 65536 ≤ abs(s2i(sho)) ⊦ s2i(sho) % 65536 = s2i(sho), s2i(sho) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: short-nle-01: ⊦ ¬ s2i(sho) ≤ ~65536;%short-max: ⊦ ¬ 65536 ≤ s2i(sho);%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ j ≤ j0 ∧ 0 < j → i % j ≠ j0;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 → abs(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)