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Proof step 9 from proof mod-rec (previous step)

i1 = i2 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j, i0 * j + j0 = i1 + j, 0 < j, 0 ≤ j0, 0 < i1 + j, j0 < i1 + j, 0 < i0, j0 < j, 0 ≤ i1 ⊦ j0 = j1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
i0 * j + j0 = j * (i2 + 1) + j1, 0 < i0 * j + j0, 0 ≤ j0, j1 < j, 0 ≤ i2, 0 ≤ j1, j0 < j, 0 < i0, 0 < j ⊦ j0 = j1

Rule argument

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%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%succ-rmerge: ⊦ i * j + i = i * (j + 1); from specification int-mult