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Proof step 27 from proof longin-mult-01 (previous step)

¬(0 ≤ abs(i) ∧ 0 ≤ abs(j) ∧ abs(i) ≤ 2147483647 ∧ abs(j) ≤ 2147483647), 0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦ abs(i) * abs(j) ≤ 2147483647 * 2147483647

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
0 < abs(i) * abs(j), 4611686014132420609 < abs(i) * abs(j), 9223372036854775807 < i * j, ~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647, 0 < i * j ⊦ ¬ 2147483647 < abs(i) ∧ ¬ 2147483647 < abs(j)

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs