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Proof step 15 from proof cast-mod-pos-low (previous step)

j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1), i→n(i) ≤ # int2bits(j), 0 ≤ i ⊦ bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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: ⊦ ¬ i < i;% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 2 ^ i, j