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

0 ≤ i, 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i

User applied rule cut formula

And obtained the following new goals

Proof step 7:
i = 0, 0 ≤ i, 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i
Proof step 10:
0 ≤ i, 0 ≤ j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i

Rule argument

fma: i = 0

Additional information

Used formulas: i = 0