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Proof step 18 from proof middle-coef-larger-strongest (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: coef-same seq: ⊦ 0 ≤ j → binom_coef(j, j) = 1 subst: [j] → [2 * i] flags: rewrite, current

Additional information

Used simplifier rules: zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2 * i