intro z hz
x : ChinesePair
xs : List ChinesePair
x_coprime : (∀ a' ∈ xs, x.modulus.Coprime a'.modulus) ∧ List.Pairwise (fun x y => x.modulus.Coprime y.modulus) xs
b : ℕ
hb : ∀ x ∈ xs, b ≡ x.remainder [MOD x.modulus]
⊢ ∀ y ∈ List.map (fun x => x.modulus) xs, x.modulus.Coprime y
x : ChinesePair
xs : List ChinesePair
x_coprime : (∀ a' ∈ xs, x.modulus.Coprime a'.modulus) ∧ List.Pairwise (fun x y => x.modulus.Coprime y.modulus) xs
b : ℕ
hb : ∀ x ∈ xs, b ≡ x.remainder [MOD x.modulus]
z : ℕ
hz : z ∈ List.map (fun x => x.modulus) xs
⊢ x.modulus.Coprime z