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Proof step 2 from proof short-add-pos (previous step)

s2i(sho) + s2i(sho0) ≤ 32767, 0 ≤ s2i(sho), 0 ≤ s2i(sho0) ⊦ s2i(i2s(s2i(sho) + s2i(sho0))) = s2i(sho) + s2i(sho0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i

Rule argument

name: num-issi rotate: F subst: [i] → [s2i(sho) + s2i(sho0)]

Additional information

Used simplifier rules: short-add-min-02: ⊦ 0 ≤ s2i(sho0) → ¬ s2i(sho0) + s2i(sho1) < ~32768;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); Used terms: s2i(sho) + s2i(sho0)