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Proof step 4 from proof modmod-mult (previous step)

i = i1 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j, 0 ≤ i, 0 ≤ i0, 0 < j ⊦ (j0 * i0 % j) % j = (i * i0) % j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: mod-shift: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i * i0 % j) % j = (i * i0) % j;%forward-le-01: ⊦ 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%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult