module Projections;

type Maybe (A : Type) :=
  | nothing : Maybe A
  | just : A -> Maybe A;

type T := t : T;

module M;
  type RecA (A B : Type) :=
    mkRecA {
      arg : Maybe (RecB B A);
      arg2 : A
    };

  type RecB (A B : Type) :=
    mkRecB {
      arg : RecA B A;
      arg2 : T
    };

  p1 : RecA T (Maybe T) :=
    mkRecA@{
      arg :=
        just
          mkRecB@{
            arg :=
              mkRecA@{
                arg := nothing;
                arg2 := t
              };
            arg2 := t
          };
      arg2 := t
    };
end;

p3 : T := M.RecA.arg2 M.p1;

open M;

p2 : T := RecA.arg2 p1;

open M.RecA;

p4 : T := arg2 p1;

module M2;
  type Pair (A B : Type) :=
    mkPair {
      fst : A;
      snd : B
    };

  open Pair public;
end;

proj1 {A B : Type} (p : M2.Pair A B) : A := M2.fst p;

import Stdlib.Data.Int open;
import Stdlib.Data.Int.Ord as Int;

x : _ := 1 Int.== 1;