n ν : ℕ
x : ↑I
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
n ν : ℕ
x : ↑I
⊢ 0 ≤ ↑(bernstein n ν) x
simp only [bernstein_apply]
n ν : ℕ
x : ↑I
h₁ : 0 ≤ ↑x
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
n ν : ℕ
x : ↑I
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
have h₁ : (0:ℝ) ≤ x := by unit_interval
n ν : ℕ
x : ↑I
h₁ : 0 ≤ ↑x
h₂ : 0 ≤ 1 - ↑x
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
n ν : ℕ
x : ↑I
h₁ : 0 ≤ ↑x
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
have h₂ : (0:ℝ) ≤ 1 - x := by unit_interval
no goals
n ν : ℕ
x : ↑I
h₁ : 0 ≤ ↑x
h₂ : 0 ≤ 1 - ↑x
⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)
positivity
no goals
n ν : ℕ
x : ↑I
⊢ 0 ≤ ↑x
unit_interval
no goals
n ν : ℕ
x : ↑I
h₁ : 0 ≤ ↑x
⊢ 0 ≤ 1 - ↑x
unit_interval