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Proof step 14 from proof le-abs-numerator (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 < i0 * (j + 1) + j0

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%zero-gr-02: ⊦ 0 ≤ i → (0 < i * j ↔ ¬ ¬(0 < j ∧ i ≠ 0)); from specification int-mult%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: 0 < i0 * (j + 1) + j0