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Proof step 28 from proof ushort-plus (previous step)

0 ≤ s2i(i2s(s2i(sho) + s2i(sho0))), s2i(sho) < 0, 0 ≤ s2i(sho0), s2i(sho) + s2i(sho0) < 0 ⊦ s2i(i2s(s2i(sho) + s2i(sho0))) = 65536 + s2i(sho) + s2i(sho0)

User applied rule insert rewrite lemma

And obtained the following new goals

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;%short-add-max-01: ⊦ s2i(sho1) < 0 → ¬ 32767 < s2i(sho0) + s2i(sho1);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i = i + j ↔ j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: s2i(sho) + s2i(sho0)