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Proof step 12 from proof cast-mult-add-h (previous step)

0 = i0 + 2 ^ i, 0 < i, i0 < 0 ⊦ 0 = i, cast(i, i0) = 0

User applied rule cut formula

And obtained the following new goals

Proof step 13:
i0 = ~1 * 2 ^ i, 0 = i0 + 2 ^ i, 0 < i, i0 < 0 ⊦ 0 = i, cast(i, i0) = 0

Rule argument

fma: i0 = ~1 * 2 ^ i

Additional information

Used simplifier rules: ⊦ i * ~1 = ~ i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ~ i = j ↔ i + j = 0;% ⊦ i + j = j + i; Used formulas: i0 = ~1 * 2 ^ i