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Proof step 31 from proof noeth-modlep (previous step)

0 ≤ i1, 0 < j2, j0 < j2, 0 ≤ j0, i0 < i, i1 < j2, j0 ≤ i1, i1 * i + i ≤ (i1 * i0 + 1 * i0) + j0 ⊦ i1 * i ≤ i1 * i0 + j0 ∧ j0 < i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ler: ⊦ i ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%int-simp-08: ⊦ i < i1 ∧ i2 < i3 → (i1 + i3 ≤ i + i2 ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2