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Proof step 55 from proof ushort-band-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ (i - j) * j0 = i * j0 - j * j0
Proof step 57:
s2i(sho) = 256 * (j0 - 1), 255 + j0 = i * 256 + j, 0 ≤ j, ~255 < j0, j0 < 0, j < 256, 0 < i ⊦ j0 = (i * 256 - 1 * 256) + j + 1, i = 0, ~255 = j0, 255 + j0 = j

Rule argument

seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [256, 1, i] rotate: F spec: int-mult inst: name: dist-sub-split

Additional information

Used terms: 256, 1, i