Notations2.out

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 y, P x y
     : (nat -> nat -> Prop) -> nat -> Prop
∃ n p : nat, n + p = 0
     : Prop
let a := 0 in
∃ (x y : nat) (b := 1) (c := b) (d := 2) (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
                 | list1 => 0
                 | _ => 2
                 end
     : list(nat) -> nat
λ n : list(nat),
match n with
| list1 => 0
| nil | 0 :: _ | 1 :: _ :: _ | plus2 _ :: _ => 2
end
     : list(nat) -> nat
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
# x : nat => # H : x <= 0 => exist (le x) 0 H
     : ∀ x : nat, x <= 0 -> {x0 : nat | x <= x0}
exist (Q x) y conj
     : {x0 : A | Q x x0}
% i
     : nat -> nat
% j
     : nat -> nat
{1, 2}
     : nat -> Prop
a#
     : Set
a#
     : Set
a≡
     : Set
a≡
     : Set
.≡
     : Set
.≡
     : Set
.a#
     : Set
.a#
     : Set
.a≡
     : Set
.a≡
     : Set
.α
     : Set
.α
     : Set
# a : .α =>
# b : .α =>
let res := 0 in
for i from 0 to a updating (res)
{{for j from 0 to b updating (res) {{S res}};; res}};; res
     : .α -> .α -> .α