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Proof step 2 from proof mod-nle-02 (previous step)

j0 + 1 < j, j0 + j ≤ 0, 0 < j, i % j ≤ j0, i % j < 0, j0 < 0, j0 < j, i % j + 1 < j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 3:
i < 0, j0 + 1 < j, j0 + j ≤ 0, 0 < j, i % j ≤ j0, i % j < 0, j0 < 0, j0 < j, i % j + 1 < j ⊦

Rule argument

fma: i < 0

Additional information

Used simplifier rules: mod-zero-01: ⊦ 0 < j ∧ 0 ≤ i → ¬ i % j < 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used formulas: i < 0