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Proof step 2 from proof modeq-pos-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 < j0, 0 < j, 0 < i0, j0 ≤ i0 * j ⊦ j0 % j = 0, j = (i0 * j - j0) % j + j0 % j

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 0 = i; (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (s)