## Stream: math-comp analysis

### Topic: Induced functions

#### Julien Puydt (Dec 06 2022 at 10:47):

Still trying to get my brain around functions.v, there's a typical situation I don't see how to handle: an induced function.

Here is a small sample code to discuss the issue at hand:

From mathcomp Require Import all_ssreflect.
From mathcomp.analysis Require Import boolp classical_sets.

Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.

Open Scope classical_set_scope.

Section InitialProblem.

Variable X Y Z: Type.
Variable A: set X.
Variable f: A -> Y.
Variable B: set Y.
Variable g: B -> Y.
Hypothesis composable: forall a, f a \in B.

Variable a: A.
Check f a.
Fail Check (g \o f) a. (* as expected *)

(* FIXME: how to turn the fact f a \in B into some kind of typing judgement f a: B?
=> the question doesn't make sense as-is, but the situation is pretty usual in mathematics
*)

End InitialProblem.

Section MinimalProblem.

Variable Y: Type.
Variable B: set Y.
Variable b: Y.
Hypothesis bB: b \in B.

(* FIXME: better question: from this data, how to build a whatever b bB of type B ? *)

(* val is essentially the reverse, if I get it right *)

End MinimalProblem.


Last updated: Feb 05 2023 at 13:02 UTC