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Proof step 4 from proof modeq-pos (previous step)

j ≠ 0, j0 < j, 0 ≤ j0, 0 < j, 0 ≤ i0 ⊦ i0 * j + j0 - (i0 * j + j0) / j * j = j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j0 < j, 0 ≤ j0, 0 < j, 0 ≤ i0 ⊦ j = 0, i0 = (i0 * j + j0) / j

Rule argument

Additional information

Used simplifier rules: 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%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs