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Proof step 4 from proof modeqp (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
(j * i1 + j) + j0 = i0 * j + j1, j0 < j, j1 < j, 0 < j, 0 ≤ j0, 0 ≤ j1, ∀ j, j0, i0, j1. i1 * j + j0 = i0 * j + j1 ∧ j0 < j ∧ j1 < j ∧ 0 < j ∧ 0 ≤ j0 ∧ 0 ≤ j1 → i1 = i0 ∧ j0 = j1 ⊦ i1 + 1 = i0 ∧ j0 = j1

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% ⊦ i +1 = i + 1; (s)