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Proof step 13 from proof divide-by-10 (previous step)

0 ≤ i ∧ 0 < 10 → (∃ i0, j0. i = i0 * 10 + j0 ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ j0 < 10), i ≤ 65536, 0 ≤ i ⊦ (i * 52429) / 524288 = i / 10

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 ≤ j, 0 ≤ i0, j < 10, i0 * 10 + j ≤ 65536 ⊦ ((i0 * 10 + j) * 52429) / 524288 = i0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ i0 < j → (j * i + i0) / j = i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;