feat(library/algebra/ordered_field.lean): add ordered fields

library/algebra/field.lean

@@ -315,8 +315,9 @@ section discrete_field
   include s
   variables {a b c : A}
 
-  definition decidable_eq [instance] (a b : A) : decidable (a = b) :=
-  @discrete_field.decidable_equality A s a b
+  -- name clash with order
+  definition decidable_eq' [instance] (a b : A) : decidable (a = b) :=
+    @discrete_field.decidable_equality A s a b
 
   theorem discrete_field.eq_zero_or_eq_zero_of_mul_eq_zero
     (x y : A) (H : x * y = 0) : x = 0 ∨ y = 0 :=

library/algebra/ordered_field.lean

@@ -0,0 +1,48 @@
+/-
+Copyright (c) 2014 Robert Lewis. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.ordered_field
+Authors: Robert Lewis
+
+Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak
+order and an associated strict order. Our numeric structures (int, rat, and real) will be instances
+of "linear_ordered_comm_ring". This development is modeled after Isabelle's library.
+-/
+
+import algebra.ordered_ring algebra.field
+open eq eq.ops
+
+namespace algebra
+          
+structure ordered_field [class] (A : Type) extends ordered_ring A, field A
+
+section ordered_field
+  
+  variable {A : Type}
+  variables [s : ordered_field A] {a b c : A}
+  include s
+
+  theorem div_pos_of_pos (H : a > 0) : 1 / a > 0 :=
+    sorry
+
+  theorem div_neg_of_neg (H : a < 0) : 1 / a < 0 :=
+    sorry
+
+  theorem le_of_div_le (H : a > 0) (Hl : 1 / a ≤ 1 / b) : b ≤ a :=
+    sorry
+
+  theorem lt_of_div_lt (H : a > 0) (Hl : 1 / a < 1 / b) : b < a :=
+    sorry
+
+  theorem le_of_div_le_neg (H : b < 0) (Hl : 1 / a ≤ 1 / b) : b ≤ a :=
+    sorry
+
+  theorem lt_of_div_lt_pos (H : b < 0) (Hl : 1 / a < 1 / b) : b < a :=
+    sorry
+
+  theorem pos_iff_div_pos : a > 0 ↔ 1 / a > 0 :=
+    sorry
+
+end ordered_field
+end algebra