2 3 : PAIR 2 [+] 3 : nat forall (A : Set) (le : A -> A -> Prop) (x y : A), le x y \/ le y x : Prop match (0, 0, 0) with | (x, y, z) => x + y + z end : nat let '(a, _, _) := (2, 3, 4) in a : nat exists myx y : bool, myx = y : Prop fun (P : nat -> nat -> Prop) (x : nat) => exists x0, P x x0 : (nat -> nat -> Prop) -> nat -> Prop ∃ n p : nat, n + p = 0 : Prop let a := 0 in ∃ x y : nat, let b := 1 in let c := b in let d := 2 in ∃ z : nat, let e := 3 in let f := 4 in x + y = z + d : Prop ∀ n p : nat, n + p = 0 : Prop λ n p : nat, n + p = 0 : nat -> nat -> Prop λ (A : Type) (n p : A), n = p : ∀ A : Type, A -> A -> Prop λ A : Type, ∃ n p : A, n = p : Type -> Prop λ A : Type, ∀ n p : A, n = p : Type -> Prop let' f (x y : nat) (a:=0) (z : nat) (_ : bool) := x + y + z + 1 in f 0 1 2 : bool -> nat λ (f : nat -> nat) (x : nat), f(x) + S(x) : (nat -> nat) -> nat -> nat Notation plus2 n := (S(S(n))) λ n : list(nat), match n with | nil => 2 | 0 :: _ => 2 | list1 => 0 | 1 :: _ :: _ => 2 | plus2 _ :: _ => 2 end : list(nat) -> nat # x : nat => x : nat -> nat # _ : nat => 2 : nat -> nat