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Proof step 6 from proof bint-band-011x (previous step)

i ≤ 2147483647, 0 ≤ i ⊦ band(i, 2 ^ 32 - 1) = i

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 ≤ i ∧ 0 ≤ 32, i ≤ 2147483647, 0 ≤ i ⊦ i % 2 ^ 32 = i

Rule argument

seq: ⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i subst: [i, j] → [32, i] rotate: F spec: intops inst: name: band-011x-pos

Additional information

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