diff options
| -rw-r--r-- | theories/Logic/ClassicalUniqueChoice.v | 13 |
1 files changed, 11 insertions, 2 deletions
diff --git a/theories/Logic/ClassicalUniqueChoice.v b/theories/Logic/ClassicalUniqueChoice.v index 67b853be94..6389e447f3 100644 --- a/theories/Logic/ClassicalUniqueChoice.v +++ b/theories/Logic/ClassicalUniqueChoice.v @@ -46,9 +46,10 @@ Qed. Require Import Setoid. -Theorem classic_set : ((forall P:Prop, {P} + {~ P}) -> False) -> False. +Theorem classic_set_in_prop_context : + forall C:Prop, ((forall P:Prop, {P} + {~ P}) -> C) -> C. Proof. -intro HnotEM. +intros C HnotEM. set (R := fun A b => A /\ true = b \/ ~ A /\ false = b). assert (H : exists f : Prop -> bool, (forall A:Prop, R A (f A))). apply unique_choice. @@ -80,3 +81,11 @@ destruct (f P). assumption. Qed. +Corollary not_not_classic_set : + ((forall P:Prop, {P} + {~ P}) -> False) -> False. +Proof. +apply classic_set_in_prop_context. +Qed. + +(* Compatibility *) +Notation classic_set := not_not_classic_set (only parsing). |