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Proof step 30 from proof divide-by-10 (previous step)

26214 * 10 + j ≤ i0 * 10 + j, 0 < 52429 * j + 2 * i0, 524288 ≤ 52429 * j + 2 * i0, 0 ≤ 52429 * j + 2 * i0, i0 * 10 + j ≤ 65536, 0 ≤ i0, 0 ≤ j, 26214 ≤ i0, j ≤ 9, 0 < i0 ⊦ 26214 * 10 + j ≤ 65536

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] → [26214 * 10 + j, i0 * 10 + j, 65536] flags: rewrite

Additional information

Used simplifier rules: ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ ¬ i ≤ j ↔ j < i;%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);% ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: 26214 * 10 + j, i0 * 10 + j, 65536