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Proof step 5 from proof mod-add-zero (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i % j + j * i1 = 0, 0 < i1, 0 < j, 0 ≤ i, j * i1 ≥ 0 ⊦ i1 = 0

Rule argument

fma: j * i1 ≥ 0

Additional information

Used simplifier rules: ⊦ i ≥ j ↔ ¬ i < j; (s)% ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)% ⊦ i < j → ¬ j < i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: j * i1 ≥ 0