Library Coq.Logic.ExtensionalityFacts
Some facts and definitions about extensionality
 
We investigate the relations between the following extensionality principles
 
 
Table of contents
 
1. Definitions
 
2. Functional extensionality <-> Equality of projections from diagonal
 
3. Functional extensionality <-> Unicity of inverse bijections
 
4. Functional extensionality <-> Bijectivity of bijective composition
 
- Functional extensionality
- Equality of projections from diagonal
- Unicity of inverse bijections
- Bijectivity of bijective composition
Set Implicit Arguments.
The diagonal over A and the one-one correspondence with A 
Record Delta A := { pi1:A; pi2:A; eq:pi1=pi2 }.
Definition delta {A} (a:A) := {|pi1 := a; pi2 := a; eq := eq_refl a |}.
Lemma diagonal_projs_same_behavior : forall A (x:Delta A), pi1 x = pi2 x.
Lemma diagonal_inverse1 : forall A, is_inverse (A:=A) delta pi1.
Lemma diagonal_inverse2 : forall A, is_inverse (A:=A) delta pi2.
Functional extensionality 
Equality of projections from diagonal 
Unicity of bijection inverse 
Bijectivity of bijective composition 
    
  