+set "baseuri" "cic:/matita/tests/rewrite/".
+
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "leibnitz's equality".
alias symbol "plus" (instance 0) = "natural plus".
\forall a,b:nat.
a = b \to b + a + b + a= (\lambda j.((\lambda w.((\lambda x.x + b + w + j) a)) b)) a.
intros.
-rewrite right H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
+rewrite < H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
-rewrite right H in \vdash (? ? % ?).
+rewrite < H in \vdash (? ? % ?).
-simplify in \vdash (? ? ? ((\lambda x.((\lambda y.%) ?)) ?)).
+simplify in \vdash (? ? ? ((\lambda _.((\lambda _.%) ?)) ?)).
-rewrite right H in \vdash (? ? ? (% ?)).
+rewrite < H in \vdash (? ? ? (% ?)).
simplify.
reflexivity.
qed.
+