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Proof step 14 from proof divide-by-10 (previous step)

0 ≤ j, 0 ≤ i0, j < 10, i0 * 10 + j ≤ 65536 ⊦ ((i0 * 10 + j) * 52429) / 524288 = i0

User applied rule cut formula

And obtained the following new goals

Proof step 15:
(i0 * 10 + j) * 52429 = 8 * i0 * 2 ^ 16 + i0 * (2 * 2 ^ 16 - 10 - 10 * 13106) + j * (2 ^ 16 - 1 - 13106), 0 ≤ j, 0 ≤ i0, j < 10, i0 * 10 + j ≤ 65536 ⊦ ((i0 * 10 + j) * 52429) / 524288 = i0

Rule argument

fma: (i0 * 10 + j) * 52429 = 8 * i0 * 2 ^ 16 + i0 * (2 * 2 ^ 16 - 10 - 10 * 13106) + j * (2 ^ 16 - 1 - 13106)

Additional information

Used simplifier rules: ⊦ i * j + i * j0 = i * (j + j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); Used formulas: (i0 * 10 + j) * 52429 = 8 * i0 * 2 ^ 16 + i0 * (2 * 2 ^ 16 - 10 - 10 * 13106) + j * (2 ^ 16 - 1 - 13106)