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Diffstat (limited to 'theories/Logic/PropExtensionality.v')
| -rw-r--r-- | theories/Logic/PropExtensionality.v | 24 |
1 files changed, 24 insertions, 0 deletions
diff --git a/theories/Logic/PropExtensionality.v b/theories/Logic/PropExtensionality.v new file mode 100644 index 00000000..80dd4e85 --- /dev/null +++ b/theories/Logic/PropExtensionality.v @@ -0,0 +1,24 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) + +(** This module states propositional extensionality and draws + consequences of it *) + +Axiom propositional_extensionality : + forall (P Q : Prop), (P <-> Q) -> P = Q. + +Require Import ClassicalFacts. + +Theorem proof_irrelevance : forall (P:Prop) (p1 p2:P), p1 = p2. +Proof. + apply ext_prop_dep_proof_irrel_cic. + exact propositional_extensionality. +Qed. + |