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Proof step 16 from proof add-div-mult (previous step)

i0 = i2 * j + j1 ∧ 0 ≤ j1 ∧ j1 < j ∧ 0 ≤ i2, j0 < j, 0 ≤ i0, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ j0 + i0, (j0 + j1) / j = 1 ∨ (j0 + j1) / j = 0 ⊦ i2 + (j0 + j1) / j = (j0 + i0) / j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ j1, 0 ≤ i2, 0 ≤ j0 + i2 * j + j1, (j0 + j1) / j = 1 ∨ (j0 + j1) / j = 0 ⊦ i2 + (j0 + j1) / j = (j0 + i2 * j + j1) / j

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%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%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult