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Proof step 13 from proof mod-div-ls (previous step)

j0 + 1 = j, j0 < j, 0 < i1, 0 < j, i0 < i1, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j, 0 ≤ i2, 0 ≤ j0, i1 ≤ (i0 + i1 * j0) / j, 0 ≤ i0, i1 ≤ (i1 * j) / j ⊦ i0 + i1 * j0 < i1 * j ∧ (i1 * j) % j = 0 ∧ 0 ≤ i0 + i1 * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0;%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); (s)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + 0 = i; (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ i * 0 = 0; (s)% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ i ≤ i; (s)% ⊦ i + ~ j = i - j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i * ~1 = ~ i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; (s)