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Proof step 13 from proof noeth-modlep (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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;%add-zero: ⊦ i + 0 = i; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%negle-13: ⊦ ~ i ≤ j ↔ 0 ≤ i + j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%subsub: ⊦ ~ i - j = ~(i + j); from specification int-abs