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Proof step 34 from proof byte-mult-256 (previous step)

~128 ≤ j0 ∧ j0 ≤ 127, ~256 ≤ j0, 0 < i, ~256 < j0, j0 < 0 ⊦ i = 0, b2i(i2b(256 + j0)) = j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 127 < i ∧ i < 256 → b2i(i2b(i)) = i - 256

Rule argument

name: bib-upper rotate: F subst: [i] → [256 + j0]

Additional information

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