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Proof step 7 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

Proof step 8:
i1 -1 * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j, 0 < j, ∀ j, j0, i0, j1. i1 * j + j0 = i0 * j + j1 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ j1 ∧ j1 < j ∧ 0 < j → i1 = i0 ∧ j0 = j1 ⊦ i0 + 1 = i1 ∧ j0 = j1

Rule argument

Additional information

Used simplifier rules: succ-01: ⊦ i +1 = i + 1; from specification int-basic2%pred: ⊦ i = j -1 ↔ i +1 = j; from specification int-basic1