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Proof step 15 from proof modmod-pos (previous step)

¬(0 < j * j0 ∧ 0 ≤ j2 * j + j1 ∧ j2 * j + j1 < j * j0), j2 < j0, j1 < j, 0 < j, 0 ≤ j1, 0 ≤ j2, 0 ≤ i1, 0 < j0 ⊦ (j2 * j + j1) % (j * j0) = j1 + j2 * j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; 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%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult