\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.%) ?)) ?)).
-rewrite right H in \vdash (? ? ? (% ?)).
+rewrite < H in \vdash (? ? ? (% ?)).
simplify.
reflexivity.
qed.