NotBad4U

// require open test.Z Stdlib.Set Stdlib.Prop;
require open tests.OK.Z tests.OK.Pos tests.OK.Set;

constant symbol R : TYPE;

symbol var : ℤ → ℤ → R;
/* semantics: [var k x] = k * x
note that the second argument could be any type that has a ring structure
(we then would take R : TYPE → TYPE) */
constant symbol cst:ℤ → R;

NotBad4U

require open Stdlib.Nat Stdlib.Z Stdlib.Set Stdlib.Prop Stdlib.Bool Stdlib.Comp Stdlib.List;

constant symbol R : TYPE;

constant symbol cst:ℤ → R;

symbol var : ℤ → ℕ → R;
/* semantics: [var k x] = k * x
note that the second argument could be any type that has a ring structure
(we then would take R : TYPE → TYPE) */

NotBad4U

require open Stdlib.Z Stdlib.Set Stdlib.Prop;

constant symbol R : TYPE;

symbol var : ℤ → ℤ → R;
/* semantics: [var k x] = k * x
note that the second argument could be any type that has a ring structure
(we then would take R : TYPE → TYPE) */
constant symbol cst:ℤ → R;
symbol opp:R → R;

NotBad4U

require open Stdlib.Prop;
require open Stdlib.FOL;
require open Stdlib.HOL;
require open Stdlib.Eq;
require open Stdlib.Set;
require open Stdlib.Z;
require open Stdlib.Pos;
require open Stdlib.Bool;
require open Stdlib.Comp;
require open Stdlib.Impred;

NotBad4U

require open Stdlib.Prop;
require open Stdlib.FOL;
require open Stdlib.Eq;
require open Stdlib.Nat;
require Stdlib.Bool;
require open Stdlib.Set;
require open Stdlib.List;

inductive prop: TYPE ≔
|pTrue: prop

NotBad4U

require open Stdlib.Set Stdlib.Prop Stdlib.FOL Stdlib.Eq Stdlib.Pos Stdlib.Bool;



inductive ℤ : TYPE ≔ // \BbbZ
| Z0 : ℤ
| Zpos : ℙ → ℤ
| Zneg : ℙ → ℤ;

constant symbol int : Set;

NotBad4U

require open Stdlib.FOL;
require open Stdlib.Prop;
require open Stdlib.Set;
require open Stdlib.Nat;
require open Stdlib.Bool;
require open Stdlib.Eq;
require open Stdlib.Z;
require open Stdlib.List;

// References use

NotBad4U

// PRELUDE ##############
// Définitions intuitioniste nécessaires pour illustrer le problème dans Classic.

constant symbol Prop : TYPE;

injective symbol π : Prop → TYPE; // `p

constant symbol ∨ : Prop → Prop → Prop; notation ∨ infix left 6; // \/ or \vee

constant symbol ∨ᵢ₁ [p q] : π p → π (p ∨ q);

NotBad4U

From Coq Require Import Bool.Bool.
From Coq Require Import Arith.Arith.
From Coq Require Import Arith.EqNat.
From Coq Require Import Arith.PeanoNat. Import Nat.
From Coq Require Import Lia.
Require Export Coq.Strings.String.
From Coq Require Import Logic.FunctionalExtensionality.
From Coq Require Import Lists.List.
Import ListNotations.

NotBad4U

trait Category<'a> { // A
    type Y<A: 'a, B: 'a>; // B
    
    fn id<A: 'a>() -> Self::Y<A, A>;
    
    fn compose<A:'a,B: 'a, C:'a>(f: Self::Y<A, B>, g: Self::Y<B, C>) -> Self::Y<A, C>;
}

struct WrapperFunc;