clutch.prob.monad.zero

#[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 giryM_zero.
  Context {d} {T : measurableType d}.
  Context `{R : realType}.
  Notation giryM := (giryM (R := R)).
  Local Open Scope classical_set_scope.

  Local Definition giryM_zero_def : giryM T := mzero.

End giryM_zero.

Definition giryM_zero {R : realType} {d} {T : measurableType d} : @giryM R _ T :=
  giryM_zero_def.

Definition giryM_zero_eval {R : realType} {d} {T : measurableType d} :
    forall t : set T, @giryM_zero R _ _ t = 0%R.
Proof. done. Qed.