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Proof step 5 from proof int2bits-2pot-04 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
j < 0, 0 ≤ i, j * 2 ^ i < 0, j * 2 ^ i < i ⊦ j = 0, int2bits(j * 2 ^ i) = int2bits(j) + mklist(false, i→n(i))

Rule argument

fma: j < 0

Additional information

Used simplifier rules: ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ 2 ^ i < 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used formulas: j < 0