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Proof step 1 from proof mult-05 (conclusion)

⊦ 0 < i0 ∧ i0 < j ∧ 0 < i → (j * i - i0) / j = i - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i0 < j, 0 < i0, 0 < j, 1 < j, 0 < i ⊦ i = (j * i - i0) / j + 1

Rule argument

Additional information

Used simplifier rules: trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs