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Proof step 1 from proof ushort-band-03 (conclusion)

⊦ band(s2i(sho), 65535) = us2i(sho)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → band(i, 65535) = i % 65536 subst: [i] → [s2i(sho)] rotate: F spec: intops inst: name: band-65535-pos

Additional information

Used simplifier rules: short-011x-neg: ⊦ s2i(sho) < 0 → band(s2i(sho), 65535) = s2i(sho) + 65536;%ushort-neg: ⊦ s2i(sho) < 0 → us2i(sho) = 2 ^ 16 + s2i(sho);%short-mod: ⊦ s2i(sho) % 65536 = s2i(sho);%ushort-pos: ⊦ 0 ≤ s2i(sho) → us2i(sho) = s2i(sho);%short-equal: ⊦ s2i(shoi) = s2i(shoj) ↔ shoi = shoj;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: s2i(sho)