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Proof step 33 from proof middle-coef-larger-strongest (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [2 * i - 1] flags: rewrite

Additional information

Used simplifier rules: sub-ls: ⊦ i - j < i0 ↔ i < j + i0; 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%nummult-ls: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i); from specification int-div%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs Used terms: 2 * i - 1