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Proof step 13 from proof mod-add-zero (previous step)

j0 > 0, j * i1 > 0, j0 + j * i1 = 0, j0 < j, 0 < j, 0 < i1, 0 ≤ j0, 0 ≤ i0 ⊦ j * i1 = 0, j0 = 0, i1 = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j0 + j * i1 > 0

Additional information

Used simplifier rules: zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%gr-def: ⊦ i > j ↔ j < i; from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs Used formulas: j0 + j * i1 > 0