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Proof step 5 from proof modeq-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i0 ⊦ i0 = (i0 * j + j0) / j, j = 0

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% ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); (s)% ⊦ i + j = i + i0 ↔ j = i0; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (s)