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Proof step 11 from proof longin-mult-01 (previous step)

~2147483648 * j ≤ i * j, i * j < ~9223372036854775808, ~2147483648 ≤ i, ~2147483648 ≤ j, j ≤ 2147483647, i < 0, 0 < j ⊦ ~2147483648 * j < ~(2 ^ 31 * 2 ^ 32)

User applied rule cut formula

And obtained the following new goals

Proof step 12:
~2147483648 = ~(2 ^ 31), ~2147483648 * j ≤ i * j, i * j < ~9223372036854775808, ~2147483648 ≤ i, ~2147483648 ≤ j, j ≤ 2147483647, i < 0, 0 < j ⊦ ~2147483648 * j < ~(2 ^ 31 * 2 ^ 32)

Rule argument

fma: ~2147483648 = ~(2 ^ 31)

Additional information

Used formulas: ~2147483648 = ~(2 ^ 31)