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Proof step 13 from proof prod-div-less (previous step)

i0 * j + j0 < i0 * j, i0 * i1 = i0 * j + j0, 0 ≤ i1, 0 ≤ i0, 0 ≤ j0, j0 < j, 1 < j, 0 < j, 0 < i1, 0 < i0, i1 < j, i0 < j ⊦

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%irref: ⊦ ¬ i < i; from specification int-basic1%mods-ls-04: ⊦ j0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ j0 → (i * j + j0 < i0 * j ↔ i < i0); from specification int-mult