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Proof step 3 from proof short-add-min-02 (previous step)

s2i(sho1) < 0, 0 ≤ s2i(sho0), s2i(sho0) + s2i(sho1) < 0, s2i(sho0) + s2i(sho1) < ~32768 ⊦ 0 + s2i(sho1) < ~32768

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i + j = j + i
Proof step 5:
s2i(sho1) < 0, 0 ≤ s2i(sho0), s2i(sho0) + s2i(sho1) < 0, s2i(sho0) + s2i(sho1) < ~32768 ⊦ s2i(sho1) + 0 < ~32768

Rule argument

seq: ⊦ i + j = j + i subst: [j, i] → [s2i(sho1), 0] rotate: F spec: int-basic2 inst: name: add-c

Additional information

Used terms: s2i(sho1), 0