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Proof step 31 from proof byte-law-mult-one (previous step)

j0 < 256, 0 ≤ i0, 0 ≤ j0 ⊦ i2b(j0 * j) = i2b(b2i(i2b(j0)) * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 127 < i ∧ i < 256 → b2i(i2b(i)) = i - 256
Proof step 33:
127 < j0 ∧ j0 < 256, j0 < 256, 0 ≤ i0, 0 ≤ j0 ⊦ i2b(j0 * j) = i2b((j0 - 256) * j)

Rule argument

name: bib-upper rotate: F subst: [i] → [j0]

Additional information

Used simplifier rules: byte-in: ⊦ 0 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: j0