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Proof step 19 from proof cast-add-2pot-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 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 < 2 ^ i ↔ 0 ≤ i;% ⊦ i + 0 = i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2 ^ i, j