diff options
Diffstat (limited to 'theories/Logic')
| -rw-r--r-- | theories/Logic/Description.v | 2 | ||||
| -rw-r--r-- | theories/Logic/EqdepFacts.v | 2 | ||||
| -rw-r--r-- | theories/Logic/IndefiniteDescription.v | 2 | ||||
| -rw-r--r-- | theories/Logic/SetIsType.v | 2 |
4 files changed, 4 insertions, 4 deletions
diff --git a/theories/Logic/Description.v b/theories/Logic/Description.v index 3e5d4ef0c..0fcbae42c 100644 --- a/theories/Logic/Description.v +++ b/theories/Logic/Description.v @@ -7,7 +7,7 @@ (************************************************************************) (** This file provides a constructive form of definite description; it - allows to build functions from the proof of their existence in any + allows building functions from the proof of their existence in any context; this is weaker than Church's iota operator *) Require Import ChoiceFacts. diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v index 4dfe99504..0d202eab5 100644 --- a/theories/Logic/EqdepFacts.v +++ b/theories/Logic/EqdepFacts.v @@ -320,7 +320,7 @@ Section Equivalences. [Definition Eq_rec_eq := forall (P:U -> Set) (p:U) (x:P p) (h:p = p), x = eq_rec p P x p h.] - Typically, [eq_rect_eq] allows to prove UIP and Streicher's K what + Typically, [eq_rect_eq] allows proving UIP and Streicher's K what does not seem possible with [eq_rec_eq]. In particular, the proof of [UIP] requires to use [eq_rect_eq] on [fun y -> x=y] which is in [Type] but not in [Set]. diff --git a/theories/Logic/IndefiniteDescription.v b/theories/Logic/IndefiniteDescription.v index 5424eea82..c1a1a31d7 100644 --- a/theories/Logic/IndefiniteDescription.v +++ b/theories/Logic/IndefiniteDescription.v @@ -7,7 +7,7 @@ (************************************************************************) (** This file provides a constructive form of indefinite description that - allows to build choice functions; this is weaker than Hilbert's + allows building choice functions; this is weaker than Hilbert's epsilon operator (which implies weakly classical properties) but stronger than the axiom of choice (which cannot be used outside the context of a theorem proof). *) diff --git a/theories/Logic/SetIsType.v b/theories/Logic/SetIsType.v index c0a6f9edc..4e36f8cb0 100644 --- a/theories/Logic/SetIsType.v +++ b/theories/Logic/SetIsType.v @@ -9,7 +9,7 @@ (** * The Set universe seen as a synonym for Type *) (** After loading this file, Set becomes just another name for Type. - This allows to easily perform a Set-to-Type migration, or at least + This allows easily performing a Set-to-Type migration, or at least test whether a development relies or not on specific features of Set: simply insert some Require Export of this file at starting points of the development and try to recompile... *) |