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Proof step 26 from proof band-011x-is-unsigned (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ abs(i) < j → i % j = i

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [2 ^ i, j] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j);% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j ≤ i ↔ j ≤ 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 2 ^ i, j