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Proof step 22 from proof noeth-modlep (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
0 < j2, j0 < j2, i0 < i, j0 < j, 0 < j, j ≤ j2, 0 ≤ j0, j * i ≤ j * i0 + j0, ∀ j0, j, i, i0. j0 < abs(j) ∧ abs(j) < j2 ∧ abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 → i ≤ i0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ i < j → ¬ j < i; (s)% ⊦ ¬ j < 0 → abs(j) = j; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)