clutch.prob.monad.const
Constant function measurable map
#[warning="-notation-incompatible-prefix -hiding-delimiting-key"]
From mathcomp Require Import all_boot all_algebra finmap.
#[warning="-notation-incompatible-prefix"]
From mathcomp Require Import mathcomp_extra boolp classical_sets functions reals interval_inference.
From mathcomp Require Import cardinality fsbigop.
From mathcomp.analysis Require Import ereal normedtype esum numfun measure lebesgue_measure lebesgue_integral.
From HB Require Import structures.
From clutch.prob.monad Require Export types.
From Stdlib.Logic Require Import FunctionalExtensionality.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Set Default Proof Using "Type".
Section MeasurableMap_const.
Context {d1 d2} {T1 : measurableType d1} {T2 : measurableType d2}.
Local Open Scope classical_set_scope.
Local Definition m_cst_def (t : T2) : T1 -> T2 := cst t.
Local Lemma m_cst_def_measurable (t : T2):
@measurable_fun _ _ T1 T2 setT (m_cst_def t).
Proof. apply measurable_cst. Qed.
HB.instance Definition _ (t : T2) :=
isMeasurableMap.Build _ _ T1 T2 (m_cst_def t) (m_cst_def_measurable t).
End MeasurableMap_const.
From mathcomp Require Import all_boot all_algebra finmap.
#[warning="-notation-incompatible-prefix"]
From mathcomp Require Import mathcomp_extra boolp classical_sets functions reals interval_inference.
From mathcomp Require Import cardinality fsbigop.
From mathcomp.analysis Require Import ereal normedtype esum numfun measure lebesgue_measure lebesgue_integral.
From HB Require Import structures.
From clutch.prob.monad Require Export types.
From Stdlib.Logic Require Import FunctionalExtensionality.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Set Default Proof Using "Type".
Section MeasurableMap_const.
Context {d1 d2} {T1 : measurableType d1} {T2 : measurableType d2}.
Local Open Scope classical_set_scope.
Local Definition m_cst_def (t : T2) : T1 -> T2 := cst t.
Local Lemma m_cst_def_measurable (t : T2):
@measurable_fun _ _ T1 T2 setT (m_cst_def t).
Proof. apply measurable_cst. Qed.
HB.instance Definition _ (t : T2) :=
isMeasurableMap.Build _ _ T1 T2 (m_cst_def t) (m_cst_def_measurable t).
End MeasurableMap_const.
Public definition for constant function
Definition m_cst {d1 d2} {T1 : measurableType d1} {T2 : measurableType d2} (v : T2) : measurable_map T1 T2 :=
m_cst_def v.
m_cst_def v.
Public equality for cst