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diff --git a/helm/ocaml/cic_disambiguation/doc/precedence.txt b/helm/ocaml/cic_disambiguation/doc/precedence.txt
index f8de4d7a5..09efea853 100644
--- a/helm/ocaml/cic_disambiguation/doc/precedence.txt
+++ b/helm/ocaml/cic_disambiguation/doc/precedence.txt
@@ -2,14 +2,31 @@
 Input                  Should be parsed as             Derived constraint
                                                        on precedence
 --------------------------------------------------------------------------------
-\lambda x.x y          ((\lambda x.x) y)               lambda > apply
+\lambda x.x y          \lambda x.(x y)               lambda > apply
 S x = y                  (= (S x) y)                   apply  > infix operators
 \forall x.x=x	       (\forall x.(= x x))	       infix operators > binders
+\lambda x.x \to x    \lambda. (x \to x)                \to > \lambda
 --------------------------------------------------------------------------------
 
 Precedence total order:
 
-  lambda > apply > infix operators > binders
+  apply > infix operators > to > binders
 
 where binders are all binders except lambda (i.e. \forall, \pi, \exists)
 
+to test:
+  
+./test_parser term << EOT 
+  \lambda x.x y
+  S x = y
+  \forall x.x=x
+  \lambda x.x \to x
+EOT
+  
+should respond with:
+  
+  \lambda x.(x y)
+  (eq (S x) y)
+  \forall x.(eq x x)
+  \lambda x.(x \to x)
+