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Proof step 3 from proof mod-nle (previous step)

i0 < i, 0 < j, 0 < i, j * i + i0 ≤ j, 0 ≤ i0 ⊦ i = 1 ∧ i0 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 4:
0 < i, 0 < j, i0 < i, 0 ≤ i0, j * i + i0 ≤ j, j * i + i0 - j ≤ 0 ⊦ i = 1 ∧ i0 = 0

Rule argument

fma: j * i + i0 - j ≤ 0

Additional information

Used simplifier rules: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: j * i + i0 - j ≤ 0