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Proof step 10 from proof ushort-plus (previous step)

s2i(sho) + s2i(sho0) < 0, s2i(sho0) < 0, 0 ≤ s2i(sho) ⊦ us2i(i2s(s2i(sho) + s2i(sho0))) = s2i(sho) + s2i(sho0) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 ≤ i ∧ i < 65536 → us2i(i2s(i)) = i
Proof step 12:
¬(0 ≤ s2i(sho) + s2i(sho0) ∧ s2i(sho) + s2i(sho0) < 65536), s2i(sho) + s2i(sho0) < 0, s2i(sho0) < 0, 0 ≤ s2i(sho) ⊦ us2i(i2s(s2i(sho) + s2i(sho0))) = s2i(sho) + s2i(sho0) + 65536

Rule argument

name: ushort-pos-01 rotate: F subst: [i] → [s2i(sho) + s2i(sho0)]

Additional information

Used simplifier rules: ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i = i + j ↔ j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: s2i(sho) + s2i(sho0)