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Proof step 2 from proof mod-add-zero (previous step)

i % j + j * i1 = 0, 0 ≤ i, 0 < j, 0 < i1 ⊦ i1 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 3:
i % j ≥ 0, i % j + j * i1 = 0, 0 ≤ i, 0 < j, 0 < i1 ⊦ i1 = 0

Rule argument

fma: i % j ≥ 0

Additional information

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