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Proof step 21 from proof divide-by-10 (previous step)

(8 * i0 * 2 ^ 16) % 524288 = 0 ∧ 0 ≤ 8 * i0 * 2 ^ 16 ∧ 0 ≤ i0 * (2 * 2 ^ 16 - 10 - 10 * 13106) + j * (2 ^ 16 - 1 - 13106) ∧ 0 < 524288, 0 ≤ j, 0 ≤ i0, j < 10, i0 * 10 + j ≤ 65536 ⊦ (8 * i0 * 2 ^ 16) / 524288 + (i0 * (2 * 2 ^ 16 - 10 - 10 * 13106) + j * (2 ^ 16 - 1 - 13106)) / 524288 = i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i = i + j ↔ j = 0;% ⊦ 1 * i = i;%j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;