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Proof step 2 from proof middle-coef-larger (previous step)

binom_coef(2 * i, i) < 4 ^ i / (2 * i + 1), 0 ≤ i ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
0 < i ⊦ binom_coef(2 * i, i) * 2 * i ≥ 4 ^ i
Proof step 4:
binom_coef(2 * i, i) * 2 * i ≥ 4 ^ i, binom_coef(2 * i, i) < 4 ^ i / (2 * i + 1), 0 ≤ i ⊦

Rule argument

spec: inst: name: middle-coef-larger-strongest seq: 0 < i ⊦ binom_coef(2 * i, i) * 2 * i ≥ 4 ^ i subst: [i] → [i] flags: current, []

Additional information

Used simplifier rules: coef-zero: ⊦ 0 ≤ i → binom_coef(i, 0) = 1;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i