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Proof step 65 from proof ushort-band-shift (previous step)

0 ≤ i * 256 + j0 + 255, s2i(sho) = 256 * (i * 256 + j0 - 1), j0 ≤ 0, abs(j0 - 1) < 256, ~255 ≤ i * 256 + j0, abs(j0) < 256, i < 0, i * 256 + j0 < 0 ⊦ 0 < i * 256 + j0 + 256, i = ~1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: i ≤ j + i0, j < j0 ⊦ i < j0 + i0 subst: [i, j, i0, j0] → [0, 255, i * 256 + j0, 256] rotate: F spec: int-abs inst: name: pls-01

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ¬ i < j ↔ j ≤ i; Used terms: 0, 255, i * 256 + j0, 256