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Proof step 9 from proof longin-mult-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
~2147483648 * j ≤ i * j, i * j < ~9223372036854775808, ~2147483648 ≤ i, ~2147483648 ≤ j, j ≤ 2147483647, i < 0, 0 < j ⊦

Rule argument

fma: ~2147483648 * j ≤ i * j

Additional information

Used simplifier rules: le-pos: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); from specification int-mult%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: ~2147483648 * j ≤ i * j