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Proof step 26 from proof noeth-modlep (previous step)

j = i1 + 1, 0 < j, j0 < j, i0 < i, j0 < j2, 0 < j2, j * i ≤ j * i0 + j0, 0 ≤ j0, j ≤ j2 ⊦ j0 + 1 < j ∧ i1 * i ≤ i1 * i0 + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
i1 < j2, 0 < j2, j0 < j2, i0 < i, 0 ≤ j0, (i1 + 1) * i ≤ (i1 + 1) * i0 + j0, j0 ≤ i1, 0 ≤ i1 ⊦ j0 < i1 ∧ i1 * i ≤ i1 * i0 + j0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ i < j + 1 ↔ i ≤ j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 1 ≤ j ↔ i < j; (s)