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Proof step 6 from proof div-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j0 < j, 0 < j, 0 ≤ j0, 0 < j * (i1 + 1) + j0, 0 ≤ i1 ⊦ (j * (i1 + 1) + j0) / j = i1 + 1

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%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