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Proof step 14 from proof noeth-modlep (previous step)

i0 < i, 0 < j2, j0 < j2, (~1 * i0 - j0 * i0) + i0 ≤ i + (~1 * i - j0 * i) + j0, ~1 * i0 - j0 * i0 ≤ (~1 * i - j0 * i) + 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
j0 < j2, 0 < j2, i0 < i, 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: minus-one-01: ⊦ i * ~1 = ~ i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i + 0 = i; (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ ~ i ≤ j ↔ 0 ≤ 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 + ~ j = i - j; (s)% ⊦ ~ i - j = ~(i + j); (s)