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Proof step 14 from proof mod-add-zero (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 15:
j0 + j * i1 = 0, j0 < j, 0 < j, 0 < i1, j0 > 0, j * i1 > 0, 0 ≤ i0, 0 ≤ j0 ⊦ j * i1 = 0, i1 = 0, j0 = 0, j0 + j * i1 > 0

Rule argument

fma: j0 + j * i1 > 0

Additional information

Used simplifier rules: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; (ws)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i > j ↔ j < i; (s)% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1 Used formulas: j0 + j * i1 > 0