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Proof step 4 from proof pot-div3-nls (previous step)

1 < i, 0 < i, 0 < j, j ^ i / 3 < j, 2 < i, 0 ≤ j, 2 ≤ j, j * j * j ≤ j ^ i ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 5:
2 < i, j ^ i / 3 < j, 0 < j, 0 < i, 1 < i, j * j * j ≤ j ^ i, 2 ≤ j, 0 ≤ j, (j * j * j) / 3 ≤ j ^ i / 3 ⊦

Rule argument

fma: (j * j * j) / 3 ≤ j ^ i / 3

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)%lsfc-01: 0 < i0 ⊦ i / i0 < j / i0 → i < j; (forward) from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≤ j → ¬ j < i; (s) Used formulas: (j * j * j) / 3 ≤ j ^ i / 3