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Proof step 3 from proof modeqp (previous step)

∀ j, j0, i0, j1. i1 * j + j0 = i0 * j + j1 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ j1 ∧ j1 < j ∧ 0 < j → i1 = i0 ∧ j0 = j1, i1 +1 * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j, 0 < j ⊦ i1 +1 = i0 ∧ j0 = j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: dist-rsplit: ⊦ i * (j + j0) = i * j + i * j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%succ-01: ⊦ i +1 = i + 1; from specification int-basic2