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authorGravatar Guillaume Melquiond <guillaume.melquiond@inria.fr>2014-10-27 10:28:57 +0100
committerGravatar Guillaume Melquiond <guillaume.melquiond@inria.fr>2014-10-27 10:32:11 +0100
commit6bb322f5ac542d12cf482b8bf02d2ee46c950a66 (patch)
treeef6d684f393cfa9ee0163442c7215b7524f1d07c /theories/Logic/Diaconescu.v
parenta9630535a1bbbef0a91795a8136d67fc636a9a93 (diff)
Fix some typos.
Diffstat (limited to 'theories/Logic/Diaconescu.v')
-rw-r--r--theories/Logic/Diaconescu.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v
index 0eba49a7e..0d3c54d2d 100644
--- a/theories/Logic/Diaconescu.v
+++ b/theories/Logic/Diaconescu.v
@@ -113,23 +113,23 @@ Theorem pred_ext_and_rel_choice_imp_EM : forall P:Prop, P \/ ~ P.
Proof.
intro P.
-(** first we exhibit the choice functional relation R *)
+(* first we exhibit the choice functional relation R *)
destruct AC_bool_subset_to_bool as [R H].
set (class_of_true := fun b => b = true \/ P).
set (class_of_false := fun b => b = false \/ P).
-(** the actual "decision": is (R class_of_true) = true or false? *)
+(* the actual "decision": is (R class_of_true) = true or false? *)
destruct (H class_of_true) as [b0 [H0 [H0' H0'']]].
exists true; left; reflexivity.
destruct H0.
-(** the actual "decision": is (R class_of_false) = true or false? *)
+(* the actual "decision": is (R class_of_false) = true or false? *)
destruct (H class_of_false) as [b1 [H1 [H1' H1'']]].
exists false; left; reflexivity.
destruct H1.
-(** case where P is false: (R class_of_true)=true /\ (R class_of_false)=false *)
+(* case where P is false: (R class_of_true)=true /\ (R class_of_false)=false *)
right.
intro HP.
assert (Hequiv : forall b:bool, class_of_true b <-> class_of_false b).
@@ -145,7 +145,7 @@ rewrite <- H0''. reflexivity.
rewrite Heq.
assumption.
-(** cases where P is true *)
+(* cases where P is true *)
left; assumption.
left; assumption.
@@ -154,7 +154,7 @@ Qed.
End PredExt_RelChoice_imp_EM.
(**********************************************************************)
-(** * B. Proof-Irrel. + Rel. Axiom of Choice -> Excl.-Middle for Equality *)
+(** * Proof-Irrel. + Rel. Axiom of Choice -> Excl.-Middle for Equality *)
(** This is an adaptation of Diaconescu's theorem, exploiting the
form of extensionality provided by proof-irrelevance *)