refactor(library/logic/axioms/prop_decidable.lean): simplify proof of prop_decidable (using arbitrary instead of epsilon)

library/logic/axioms/prop_decidable.lean

@@ -4,20 +4,17 @@ Released under Apache 2.0 license as described in the file LICENSE.
 
 Module: logic.axioms.prop_decidable
 Author: Leonardo de Moura
+
+Excluded middle + Hilbert implies every proposition is decidable.
 -/
 import logic.axioms.prop_complete logic.axioms.hilbert
 open decidable inhabited nonempty
 
--- Excluded middle + Hilbert implies every proposition is decidable
-
--- First, we show that (decidable a) is inhabited for any 'a' using the excluded middle
 theorem decidable_inhabited [instance] (a : Prop) : inhabited (decidable a) :=
 inhabited_of_nonempty
   (or.elim (em a)
     (assume Ha, nonempty.intro (inl Ha))
     (assume Hna, nonempty.intro (inr Hna)))
 
--- Note that decidable_inhabited is marked as an instance, and it is silently used
--- for synthesizing the implicit argument in the following 'epsilon'
 theorem prop_decidable [instance] (a : Prop) : decidable a :=
-epsilon (λd, true)
+arbitrary (decidable a)