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Proof step 43 from proof middle-coef-larger-strongest (previous step)

4 ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), i0 ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i, binom_coef(2 * i, i) < i0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: countFun-in seq: ⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0) subst: [intfun, j, i, i0] → [λ j. binom_coef(2 * i, j), 2 * i, 0, i0] flags: rewrite

Additional information

Used simplifier rules: middle-coef-largest: ⊦ j ≤ 2 * i ∧ 0 ≤ j → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, j);%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: λ j. binom_coef(2 * i, j), 2 * i, 0, i0