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Proof step 37 from proof bxor-flip-one-bit (previous step)

0 ≤ j, 0 ≤ i, 2 ^ (j + 1) < i, i < 2 ^ (j - 1), 2 ^ (j - 2) ≤ i, 0 < j ⊦ j = 0, j = 1, bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))) = [], bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))).first ∧ sgn(bitsxor(int2bits(i), false ' + true ' + mklist(false, i→n(j))))[0, false] = int2bits(i)

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 2 ^ (j + 1) < 2 ^ (j - 1)

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j = j + i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used formulas: 2 ^ (j + 1) < 2 ^ (j - 1)