diff options
| -rw-r--r-- | theories/Logic/ClassicalFacts.v | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/theories/Logic/ClassicalFacts.v b/theories/Logic/ClassicalFacts.v index 896fddc75..ad9171843 100644 --- a/theories/Logic/ClassicalFacts.v +++ b/theories/Logic/ClassicalFacts.v @@ -31,8 +31,8 @@ Table of contents: 3.1. Weak excluded middle -3.2. Gödel-Dummet axiom and right distributivity of implication over - disjunction +3.2. Gödel-Dummett axiom and right distributivity of implication over + disjunction 3 3. Independence of general premises and drinker's paradox @@ -396,7 +396,7 @@ End Proof_irrelevance_CCI. (** We show the following increasing in the strength of axioms: - weak excluded-middle - - right distributivity of implication over disjunction and Gödel-Dummet axiom + - right distributivity of implication over disjunction and Gödel-Dummett axiom - independence of general premises and drinker's paradox - excluded-middle *) @@ -533,7 +533,11 @@ Proof. Qed. (** Independence of general premises is weaker than (generalized) - excluded middle *) + excluded middle + +Remark: generalized excluded middle is preferred here to avoid relying on +the "ex falso quodlibet" property (i.e. [False -> forall A, A]) +*) Definition generalized_excluded_middle := forall A B:Prop, A \/ (A -> B). |