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.

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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;

NotBad4U

------------------------------ MODULE real ------------------------------- 

EXTENDS Naturals, Integers, Sequences, FiniteSets, FiniteSetsExt, NaturalsInduction

CONSTANT max

McNat == 0..max

(***********************************************************************)
(* Approximate sqrt(r)                                                  *)