--- a/src/Equality.v	Wed Aug 29 17:17:17 2012 -0400
+++ b/src/Equality.v	Wed Aug 29 18:26:26 2012 -0400
@@ -691,7 +691,7 @@
     JMeq_refl : JMeq x x
     ]]
 
-The identitifer [JMeq] stands for %\index{John Major equality}%"John Major equality," a name coined by Conor McBride%~\cite{JMeq}% as a sort of pun about British politics.  The definition [JMeq] starts out looking a lot like the definition of [eq].  The crucial difference is that we may use [JMeq] _on arguments of different types_.  For instance, a lemma that we failed to establish before is trivial with [JMeq].  It makes for prettier theorem statements to define some syntactic shorthand first. *)
+The identifier [JMeq] stands for %\index{John Major equality}%"John Major equality," a name coined by Conor McBride%~\cite{JMeq}% as a sort of pun about British politics.  The definition [JMeq] starts out looking a lot like the definition of [eq].  The crucial difference is that we may use [JMeq] _on arguments of different types_.  For instance, a lemma that we failed to establish before is trivial with [JMeq].  It makes for prettier theorem statements to define some syntactic shorthand first. *)
 
 Infix "==" := JMeq (at level 70, no associativity).
 
@@ -842,7 +842,7 @@
          (P : forall B0 : Type, B0 -> Type), P B b -> x == b -> P A x
 ]]
 
-The key difference is that, where the [eq] lemma is parametrized on a predicate of type [A -> Prop], the [JMeq] lemma is parameterized on a predicate of type more like [forall A : Type, A -> Prop].  To apply [eq_ind_r] with a proof of [x = y], it is only necessary to rearrange the goal into an application of a [fun] abstraction to [y].  In contrast, to apply [internal_JMeq_rew_r], it is necessary to rearrange the goal to an application of a [fun] abstraction to both [y] and _its type_.  In other words, the predicate must be _polymorphic_ in [y]'s type; any type must make sense, from a type-checking standpoint.  There may be cases where the former rearrangement is easy to do in a type-correct way, but the second rearrangement done naively leads to a type error.
+The key difference is that, where the [eq] lemma is parameterized on a predicate of type [A -> Prop], the [JMeq] lemma is parameterized on a predicate of type more like [forall A : Type, A -> Prop].  To apply [eq_ind_r] with a proof of [x = y], it is only necessary to rearrange the goal into an application of a [fun] abstraction to [y].  In contrast, to apply [internal_JMeq_rew_r], it is necessary to rearrange the goal to an application of a [fun] abstraction to both [y] and _its type_.  In other words, the predicate must be _polymorphic_ in [y]'s type; any type must make sense, from a type-checking standpoint.  There may be cases where the former rearrangement is easy to do in a type-correct way, but the second rearrangement done naively leads to a type error.
 
 When [rewrite] cannot figure out how to apply [internal_JMeq_rew_r] for [x == y] where [x] and [y] have the same type, the tactic can instead use an alternate theorem, which is easy to prove as a composition of [eq_ind_r] and [JMeq_eq]. *)