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Proof step 6 from proof zero-gr-add-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 < i1 * j + i1

Additional information

Used simplifier rules: ⊦ i + j ≤ i0 + j ↔ i ≤ i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: 0 < i1 * j + i1