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Proof step 3 from proof pot-div3-nls (previous step)

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

User applied rule cut formula

And closed the goal!

Rule argument

fma: (j * j * j) / 3 ≤ j ^ i / 3

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%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%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%div-mult-three-nls: ⊦ 2 ≤ j → ¬ (j * j * j) / 3 < j; from specification int-div Used formulas: (j * j * j) / 3 ≤ j ^ i / 3