Mercurial > cpdt > repo
diff src/Universes.v @ 392:4b1242b277b2
Typo fixes
author | Adam Chlipala <adam@chlipala.net> |
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date | Fri, 20 Apr 2012 12:49:47 -0400 |
parents | 057a29f9c773 |
children | 05efde66559d |
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--- a/src/Universes.v Thu Apr 12 18:46:55 2012 -0400 +++ b/src/Universes.v Fri Apr 20 12:49:47 2012 -0400 @@ -627,7 +627,7 @@ (** This kind of %``%#"#axiomatic presentation#"#%''% of a theory is very common outside of higher-order logic. However, in Coq, it is almost always preferable to stick to defining your objects, functions, and predicates via inductive definitions and functional programming. - In general, there is a significant burden associated with any use of axioms. It is easy to assert a set of axioms that together is %\index{inconsistent axioms}\textit{%#<i>#inconsistent#</i>#%}%. That is, a set of axioms may imply [False], which allows any theorem to proved, which defeats the purpose of a proof assistant. For example, we could assert the following axiom, which is consistent by itself but inconsistent when combined with [classic]. *) + In general, there is a significant burden associated with any use of axioms. It is easy to assert a set of axioms that together is %\index{inconsistent axioms}\textit{%#<i>#inconsistent#</i>#%}%. That is, a set of axioms may imply [False], which allows any theorem to be proved, which defeats the purpose of a proof assistant. For example, we could assert the following axiom, which is consistent by itself but inconsistent when combined with [classic]. *) Axiom not_classic : ~ forall P : Prop, P \/ ~ P.