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Proof step 10 from proof cast-law-add-pos (previous step)

0 ≤ j1, j1 < 2 ^ i, j1 < 2 ^ (i - 1), 0 ≤ j0, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, (i0 * 2 ^ i + j1) + j0) = cast(i, j1 + j0)

User applied rule cut formula

And obtained the following new goals

Proof step 11:
(i0 * 2 ^ i + j1) + j0 = i0 * 2 ^ i + j1 + j0, 0 ≤ j1, j1 < 2 ^ i, j1 < 2 ^ (i - 1), 0 ≤ j0, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, (i0 * 2 ^ i + j1) + j0) = cast(i, j1 + j0)

Rule argument

fma: (i0 * 2 ^ i + j1) + j0 = i0 * 2 ^ i + j1 + j0

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: (i0 * 2 ^ i + j1) + j0 = i0 * 2 ^ i + j1 + j0