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Proof step 2 from proof cast-mult-add-h (previous step)

0 ≤ i, 0 < i, j0 < 2 ^ i, j < 0, 0 ≤ j0 ⊦ cast(i, j * 2 ^ i + j0) = cast(i, j0)

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: j * 2 ^ i + j0 = (j + 1) * 2 ^ i + (j0 - 2 ^ i)

Additional information

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