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Proof step 17 from proof noeth-modlep (previous step)

i0 < i, 0 < j2, j0 < j2, j0 * i + i + i0 - i0 + j0 * i0 ≤ j0 + i, i + j0 * i ≤ j0 * i0 + i0 + j0, 0 ≤ j0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ ~1 = j0, (i0 + 1) * j0 ≤ i * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
j0 < j2, 0 < j2, i0 < i, i * j0 < i0 * j0 + j0, 0 ≤ j0, i + j0 * i ≤ j0 * i0 + i0 + j0, j0 * i + i + i0 - i0 + j0 * i0 ≤ j0 + i, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦ ~1 = j0

Rule argument

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≤ j ↔ ¬ j < i; (ss)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2