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Proof step 35 from proof int2bytes-first-zerobyte-01 (previous step)

j0 < 2 + 8 * i, 0 < j0, 0 ≤ i, 2 ^ (8 * i - 1) < 2 ^ (j0 - 1), j < 2 ^ (j0 - 1), 2 ^ (j0 - 2) ≤ j, 0 ≤ j, j0 < 8, 2 ^ (8 * i - 1) ≤ j, j < 2 ^ (8 * i) ⊦ j0 = 0, j0 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [j0 - 1, 8 * i - 1] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used simplifier rules: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 ≤ i → (i < 1 ↔ i = 0);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < j → (j < 2 ↔ j = 1); Used terms: j0 - 1, 8 * i - 1