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Proof step 21 from proof longin-mult-01 (previous step)

0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 22:
abs(i) * abs(j) ≤ 2147483647 * 2147483647, 0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦
Proof step 25:
0 < i * j, j ≤ 2147483647, ~2147483648 ≤ j, i ≤ 2147483647, ~2147483648 ≤ i, 9223372036854775807 < i * j ⊦ abs(i) * abs(j) ≤ 2147483647 * 2147483647

Rule argument

fma: abs(i) * abs(j) ≤ 2147483647 * 2147483647

Additional information

Used formulas: abs(i) * abs(j) ≤ 2147483647 * 2147483647