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Proof step 4 from proof longin-mult-01 (previous step)

~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647 ⊦ ~(2 ^ 63) ≤ i * j ∧ i * j ≤ 2 ^ 63 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
~2147483648 ≤ i, i ≤ 2147483647, ~2147483648 ≤ j, j ≤ 2147483647 ⊦ ¬ i * j < ~9223372036854775808 ∧ ¬ 9223372036854775807 < i * j

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs