more lemmas on div real

theories/algebra.why

@@ -89,6 +89,19 @@ theory Field
   function inv t : t
   axiom Inverse : forall x:t. x <> zero -> x * inv x = one
   function (/) (x y : t) : t = x * inv y
+
+  lemma assoc_mul_div: forall x y z:real.
+    (* todo: discard the hypothesis ? *)
+     z <> zero -> (x*y)/z = x*(y/z)
+
+  lemma assoc_div_mul: forall x y z:real.
+    (* todo: discard the hypothesis ? *)
+     y <> zero /\ z <> zero -> (x/y)/z = x/(y*z)
+
+  lemma assoc_div_div: forall x y z:real.
+    (* todo: discard the hypothesis ? *)
+     y <> zero /\ z <> zero -> x/(y/z) = (x*z)/y
+
 end
 
 theory OrderedField