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Proof step 8 from proof mod-ex-div (previous step)

i % j < 0, i % j < 0 ⊦ j = 0, i = j * i / j + i % j + j, ∃ j0. i = j * j0 + i % j + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i % j < 0 ⊦ j = 0, ∃ j0. i = j * j0 + i % j + j

Rule argument

Additional information

Used simplifier rules: eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2%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%divmod-rew: j ≠ 0 ⊦ i / j * j + i % j = i; from specification int-div