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Proof step 32 from proof divide-by-10 (previous step)

52429 * j + 2 * i0 ≤ 52429 * 9 + 2 * i0, 0 < 52429 * j + 2 * i0, 524288 ≤ 52429 * j + 2 * i0, 0 ≤ 52429 * j + 2 * i0, i0 * 10 + j ≤ 65536, j < 10, 0 ≤ i0, 0 ≤ j ⊦ 524288 ≤ 52429 * 9 + 2 * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: forward-lele seq: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1 subst: [j, j0, j1] → [524288, 52429 * j + 2 * i0, 52429 * 9 + 2 * i0] flags: rewrite

Additional information

Used simplifier rules: ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 ≤ (* j) ↔ i0 ≤ j / i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);% ⊦ i * j = j * i; Used terms: 524288, 52429 * j + 2 * i0, 52429 * 9 + 2 * i0