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Proof step 42 from proof byte-mult-256 (previous step)

i0 < 0, 0 < i, ~256 < j0, i0 < i, j0 < 0, i0 * 256 + j0 < 0, 0 < i0 + i ⊦ i = 0, i2b((i0 + i - 1) * 256 + 256 + j0) = i2b(j0), i0 + i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ 0 ≤ i ∧ 0 ≤ j → i2b(i * 256 + j) = i2b(j)
Proof step 44:
0 ≤ i0 + i - 1 ∧ 0 ≤ 256 + j0, i0 < 0, 0 < i, ~256 < j0, i0 < i, j0 < 0, i0 * 256 + j0 < 0, 0 < i0 + i ⊦ i = 0, i2b(256 + j0) = i2b(j0), i0 + i = 0

Rule argument

name: byte-mult-pos rotate: F subst: [j, i] → [256 + j0, i0 + i - 1]

Additional information

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