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Proof step 18 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 + 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

Proof step 19:
52429 * j + 2 * i0 < 0, i0 * 10 + j ≤ 65536, j < 10, 0 ≤ i0, 0 ≤ j ⊦ (i0 * 524290 + 52429 * j) / 524288 = i0

Rule argument

Additional information

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