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Proof step 8 from proof longin-mult-01 (previous step)

i < 0, i * j < ~9223372036854775808, ~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647, i * j < 0 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i * j < ~9223372036854775808, ~2147483648 ≤ i, ~2147483648 ≤ j, j ≤ 2147483647, i < 0, 0 < j ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ls-01: ⊦ i < 0 → (i * j < 0 ↔ 0 < j); from specification int-mult%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs