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Proof step 9 from proof intshiftleft-is-mult (previous step)

j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(j % 32))) = i * 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
0 < j, 0 ≤ i, i < j ⊦ i % j = i
Proof step 11:
0 < 32 ∧ 0 ≤ j ∧ j < 32, j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(j))) = i * 2 ^ j

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i % j = i subst: [j, i] → [32, j] rotate: F spec: int-div inst: name: mod-zero-03

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: 32, j