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Proof step 2 from proof div-elim-divides (previous step)

i % j = 0 ⊦ i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 = 0, 0 = j

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: divmult: j ≠ 0 ⊦ i % j = 0 → i / j * j = i;%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;% ⊦ i + 0 = i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i = i + j ↔ j = 0; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult