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Proof step 7 from proof middle-coef-larger-strongest (previous step)

2 ^ (2 * i) = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j * j0) = (i ^ j) ^ j0
Proof step 9:
0 ≤ 2 ∧ 0 ≤ i, (2 ^ 2) ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i ⊦

Rule argument

spec: int-pot inst: name: pot-pot-02 seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j * j0) = (i ^ j) ^ j0 subst: [j0, j, i] → [i, 2, 2] flags: rewrite

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i, 2, 2