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Proof step 7 from proof short-add-min (previous step)

s2i(sho0) + s2i(sho1) < 0, ¬ ~32768 + ~32768 < s2i(sho0) + s2i(sho1) ⊦ s2i(sho0) = ~32768 ∧ s2i(sho1) = ~32768

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: i < j, i0 ≤ j0 ⊦ i + i0 < j + j0 subst: [j0, j, i0, i] → [s2i(sho1), s2i(sho0), ~32768, ~32768] rotate: F spec: int-abs inst: name: ple-01

Additional information

Used simplifier rules: short-min-03: ⊦ s2i(sho) ≤ ~32768 ↔ s2i(sho) = ~32768;%short-min-01: ⊦ ¬ s2i(sho) < ~32768;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ i ∧ i < 0 → j < 0; (forward)%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;% ⊦ i - j < i0 ↔ i < j + i0; Used terms: s2i(sho1), s2i(sho0), ~32768, ~32768