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Proof step 39 from proof ushort-band-01 (previous step)

j + i * 256 = (i0 + 255) * 256 + j0 + 255, j0 < ~255, j0 < 0, ~256 < j0, j + i * 256 < 65535, i0 ≤ 0, j < 256, 0 ≤ i, 0 ≤ j ⊦ 255 + j0 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ i < j ↔ i +1 = j ∨ i +1 < j

Rule argument

seq: ⊦ i < j ↔ i +1 = j ∨ i +1 < j subst: [j, i] → [~255, j0] rotate: F spec: int-basic1 inst: name: lsrec

Additional information

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