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Proof step 33 from proof cast-mod-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ 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 < j → abs(j) = j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2 ^ i, j