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Proof step 16 from proof mod-pred-02 (previous step)

(i1 * j + j0) + 1 = i0 * j + j1, 0 < j1, 0 < j, 1 < j, j0 < j, j1 < j, j ≤ j0 + 1, ~1 ≤ i1 * j + j0, 0 ≤ i1, 0 ≤ j0 ⊦ j1 = 0, (i1 + 1) * (j0 + 1) + 0 = i0 * (j0 + 1) + j1 ∧ 0 ≤ 0 ∧ 0 < j0 + 1 ∧ 0 ≤ j1 ∧ j1 < j0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
(i1 * j + j0) + 1 = i0 * j + j1, j1 < j, j0 < j, 1 < j, 0 < j, 0 < j1, 0 ≤ j0, 0 ≤ i1, ~1 ≤ i1 * j + j0, j ≤ j0 + 1 ⊦ j1 = 0, (i1 + 1) * (j0 + 1) = i0 * (j0 + 1) + j1 ∧ j1 ≤ j0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < j + 1 ↔ i ≤ j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 0 = i; (s)