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Proof step 7 from proof noeth-modlep (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
j = ~1 - j0, j0 + j = ~1, j * i0 + i0 ≤ i + j * i + j0, 0 ≤ j + j2, j < 0, j * i0 ≤ j * i + j0, i0 < i, 0 ≤ j0, 0 < j2, j0 < j2, ∀ j, i, i0, j0. abs(j) < j2 → abs(j) * i ≤ abs(j) * i0 + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) → i ≤ i0 ⊦ j = 0

Rule argument

fma: j = ~1 - j0

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: j = ~1 - j0