diff options
author | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2014-10-27 10:28:57 +0100 |
---|---|---|
committer | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2014-10-27 10:32:11 +0100 |
commit | 6bb322f5ac542d12cf482b8bf02d2ee46c950a66 (patch) | |
tree | ef6d684f393cfa9ee0163442c7215b7524f1d07c /theories/Logic/Diaconescu.v | |
parent | a9630535a1bbbef0a91795a8136d67fc636a9a93 (diff) |
Fix some typos.
Diffstat (limited to 'theories/Logic/Diaconescu.v')
-rw-r--r-- | theories/Logic/Diaconescu.v | 12 |
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 *) |