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Proof step 7 from proof modneqp (previous step)

j1 < j, j0 < j, i < i1, 0 < j, 0 < i1, i1 * j + j1 ≤ i * i0 + j0, 0 ≤ j1, 0 ≤ j0, 0 ≤ i0, i0 ≤ j, 0 ≤ i, 0 ≤ j, i1 * j + j1 ≤ i * j + j0 ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modlep-03 seq: j * i + j0 ≤ j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [j, i1, j1, i, j0]

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ 0 ≤ i → abs(i) = i; (s) Used terms: j, i1, j1, i, j0