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Proof step 6 from proof intshiftleft-is-mult (previous step)

j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 2 ^ 5 - 1)))) = i * 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i
Proof step 8:
0 ≤ j ∧ 0 ≤ 5, j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(j % 2 ^ 5))) = i * 2 ^ j

Rule argument

name: band-011x-pos rotate: F subst: [i, j] → [5, j]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 5, j