refactor(library/algebra/order.lean): rename a field in an order structure

library/algebra/order.lean

@@ -116,7 +116,7 @@ wf.rec_on x H
 /- structures with a weak and a strict order -/
 
 structure order_pair [class] (A : Type) extends weak_order A, has_lt A :=
-(lt_iff_le_ne : ∀a b, lt a b ↔ (le a b ∧ a ≠ b))
+(lt_iff_le_and_ne : ∀a b, lt a b ↔ (le a b ∧ a ≠ b))
 
 section
   variable [s : order_pair A]
@@ -124,7 +124,7 @@ section
   include s
 
   theorem lt_iff_le_and_ne : a < b ↔ (a ≤ b ∧ a ≠ b) :=
-  !order_pair.lt_iff_le_ne
+  !order_pair.lt_iff_le_and_ne
 
   theorem le_of_lt (H : a < b) : a ≤ b :=
   and.elim_left (iff.mp lt_iff_le_and_ne H)
@@ -243,10 +243,10 @@ iff.intro
 definition strict_order_with_le.to_order_pair [instance] [coercion] [reducible] [s : strict_order_with_le A] :
   strong_order_pair A :=
 ⦃ strong_order_pair, s,
-  le_refl      := le_refl s,
-  le_trans     := le_trans s,
-  le_antisymm  := le_antisymm s,
-  lt_iff_le_ne := lt_iff_le_ne s ⦄
+  le_refl          := le_refl s,
+  le_trans         := le_trans s,
+  le_antisymm      := le_antisymm s,
+  lt_iff_le_and_ne := lt_iff_le_ne s ⦄
 
 /- linear orders -/
 

library/data/int/order.lean

@@ -229,7 +229,7 @@ section
     le_trans         := @le.trans,
     le_antisymm      := @le.antisymm,
     lt               := lt,
-    lt_iff_le_ne     := lt_iff_le_and_ne,
+    lt_iff_le_and_ne := lt_iff_le_and_ne,
     add_le_add_left  := @add_le_add_left,
     mul_nonneg       := @mul_nonneg,
     mul_pos          := @mul_pos,

library/data/nat/order.lean

@@ -158,7 +158,7 @@ section
     le_antisymm                := @le.antisymm,
     le_total                   := @le.total,
     le_iff_lt_or_eq            := @le_iff_lt_or_eq,
-    lt_iff_le_ne               := lt_iff_le_and_ne,
+    lt_iff_le_and_ne           := lt_iff_le_and_ne,
     add_le_add_left            := @add_le_add_left,
     le_of_add_le_add_left      := @le_of_add_le_add_left,
     zero_ne_one                := ne.symm (succ_ne_zero zero),

library/data/rat/order.lean

@@ -198,7 +198,7 @@ theorem mul_pos (H1 : a > 0) (H2 : b > 0) : a * b > 0 :=
 have H : pos (a * b), from pos_mul (!sub_zero ▸ H1) (!sub_zero ▸ H2),
 !sub_zero⁻¹ ▸ H
 
-definition has_decidable_lt [instance] : decidable_rel rat.lt :=
+definition decidable_lt [instance] : decidable_rel rat.lt :=
 take a b, decidable_pos (b - a)
 
 section
@@ -208,16 +208,16 @@ section
     algebra.discrete_linear_ordered_field rat :=
   ⦃algebra.discrete_linear_ordered_field,
     rat.discrete_field,
-    le_refl         := le.refl,
-    le_trans        := @le.trans,
-    le_antisymm     := @le.antisymm,
-    le_total        := @le.total,
-    lt_iff_le_ne    := @lt_iff_le_and_ne,
-    le_iff_lt_or_eq := @le_iff_lt_or_eq,
-    add_le_add_left := @add_le_add_left,
-    mul_nonneg      := @mul_nonneg,
-    mul_pos         := @mul_pos,
-    decidable_lt    := @has_decidable_lt⦄
+    le_refl          := le.refl,
+    le_trans         := @le.trans,
+    le_antisymm      := @le.antisymm,
+    le_total         := @le.total,
+    lt_iff_le_and_ne := @lt_iff_le_and_ne,
+    le_iff_lt_or_eq  := @le_iff_lt_or_eq,
+    add_le_add_left  := @add_le_add_left,
+    mul_nonneg       := @mul_nonneg,
+    mul_pos          := @mul_pos,
+    decidable_lt     := @decidable_lt⦄
 
 --  migrate from algebra with rat
 end