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Proof step 41 from proof middle-coef-larger-strongest (previous step)

4 ^ i = 2 + Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), 2 ≤ binom_coef(2 * i, i), Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)) ≤ binom_coef(2 * i, i) * (2 * i - 1), binom_coef(2 * i, i) ∈ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 < binom_coef(2 * i, i), 0 ≤ binom_coef(2 * i, i), ∀ i0. i0 ∈ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)) ∨ i0 = 1 → i0 ≤ binom_coef(2 * i, i) ⊦ 4 ^ i ≤ binom_coef(2 * i, i) + (2 * i - 1) * binom_coef(2 * i, i), i = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%int-simp-07: ⊦ i ≤ i1 ∧ i2 ≤ i3 → (i1 + i3 < i + i2 ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2