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Proof step 14 from proof mod-nls-04 (previous step)

0 < j, abs(i % j) < j, i % j < i0, i0 < 0, abs(i % j) < abs(i0), i0 + j ≤ 0 ⊦ i0 + j = 1

User applied rule cut formula

And obtained the following new goals

Proof step 15:
abs(i % j) < abs(i0), i0 < 0, i % j < i0, abs(i % j) < j, 0 < j, i0 + j ≤ 0, j ≤ abs(i0) ⊦ i0 + j = 1

Rule argument

fma: j ≤ abs(i0)

Additional information

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