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Proof step 2 from proof cast-sub-2pot (previous step)

0 < i ⊦ cast(i, 2 ^ i - j0) = cast(i, ~ j0)

User applied rule cut formula

And obtained the following new goals

Proof step 3:
2 ^ i - j0 = 1 * 2 ^ i + ~ j0, 0 < i ⊦ cast(i, 2 ^ i - j0) = cast(i, ~ j0)

Rule argument

fma: 2 ^ i - j0 = 1 * 2 ^ i + ~ j0

Additional information

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