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Proof step 29 from proof band-011x-eq (previous step)

0 ≤ i0, j < 2 ^ i0, 0 ≤ j ⊦ 2 ^ i0 = (j % 2 ^ i0 + (2 ^ i0 - 1 + j) % 2 ^ i0) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
0 < j, 0 ≤ i, i < j ⊦ i % j = i
Proof step 31:
0 < 2 ^ i0 ∧ 0 ≤ j ∧ j < 2 ^ i0, 0 ≤ i0, j < 2 ^ i0, 0 ≤ j ⊦ 2 ^ i0 = (j + (2 ^ i0 - 1 + j) % 2 ^ i0) + 1

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i % j = i subst: [j, i] → [2 ^ i0, j] rotate: F spec: int-div inst: name: mod-zero-03

Additional information

Used simplifier rules: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2 ^ i0, j