refactor(library): avoid 'context' command in the standard library

library/algebra/binary.lean

@@ -44,12 +44,12 @@ namespace binary
     definition left_commutative [reducible] {B : Type}  (f : A → B → B) := ∀ a₁ a₂ b, f a₁ (f a₂ b) = f a₂ (f a₁ b)
   end
 
-  context
+  section
     variable {A : Type}
     variable {f : A → A → A}
     variable H_comm : commutative f
     variable H_assoc : associative f
-    infixl `*` := f
+    local infixl `*` := f
     theorem left_comm : left_commutative f :=
     take a b c, calc
       a*(b*c) = (a*b)*c  : H_assoc
@@ -63,11 +63,11 @@ namespace binary
         ...   = (a*c)*b : H_assoc
   end
 
-  context
+  section
     variable {A : Type}
     variable {f : A → A → A}
     variable H_assoc : associative f
-    infixl `*` := f
+    local infixl `*` := f
     theorem assoc4helper (a b c d) : (a*b)*(c*d) = a*((b*c)*d) :=
     calc
       (a*b)*(c*d) = a*(b*(c*d)) : H_assoc

library/algebra/category/constructions.lean

@@ -79,7 +79,7 @@ namespace category
      (λ a b f, @subsingleton.elim (set_hom a b) _ _ _)
   local attribute discrete_category [reducible]
   definition Discrete_category (A : Type) [H : decidable_eq A] := Mk (discrete_category A)
-    context
+    section
     local attribute discrete_category [instance]
     include H
     theorem discrete_category.endomorphism {a b : A} (f : a ⟶ b) : a = b :=

library/algebra/ordered_group.lean

@@ -489,7 +489,7 @@ section
   abs.by_cases H1 H2
 
   -- the triangle inequality
-  context
+  section
     private lemma aux1 {a b : A} (H1 : a + b ≥ 0) (H2 : a ≥ 0) : abs (a + b) ≤ abs a + abs b :=
     decidable.by_cases
       (assume H3 : b ≥ 0,

library/data/int/basic.lean

@@ -128,8 +128,8 @@ calc
   sub_nat_nat m n = nat.cases_on 0 (of_nat (m - n)) _ : H1 ▸ rfl
     ... = of_nat (m - n) : rfl
 
-context
-attribute sub_nat_nat [reducible]
+section
+local attribute sub_nat_nat [reducible]
 theorem sub_nat_nat_of_lt {m n : ℕ} (H : m < n) :
   sub_nat_nat m n = neg_succ_of_nat (pred (n - m)) :=
 have H1 : n - m = succ (pred (n - m)), from (succ_pred_of_pos (sub_pos_of_lt H))⁻¹,
@@ -276,9 +276,9 @@ calc
     ... = abstr (repr b) : abstr_eq H
     ... = b : abstr_repr
 
-context
-attribute abstr [reducible]
-attribute dist [reducible]
+section
+local attribute abstr [reducible]
+local attribute dist [reducible]
 theorem nat_abs_abstr (p : ℕ × ℕ) : nat_abs (abstr p) = dist (pr1 p) (pr2 p) :=
 let m := pr1 p, n := pr2 p in
 or.elim (@le_or_gt n m)
@@ -458,8 +458,8 @@ have H3 : pabs (padd (repr a) (repr b)) ≤ pabs (repr a) + pabs (repr b),
   from !dist_add_add_le_add_dist_dist,
 H⁻¹ ▸ H1⁻¹ ▸ H2⁻¹ ▸ H3
 
-context
-attribute nat_abs [reducible]
+section
+local attribute nat_abs [reducible]
 theorem mul_nat_abs (a b : ℤ) : nat_abs (a * b) = #nat (nat_abs a) * (nat_abs b) :=
 int.cases_on a
   (take m,

library/data/nat/choose.lean

@@ -16,7 +16,7 @@ import data.subtype data.nat.basic data.nat.order
 open nat subtype decidable well_founded
 
 namespace nat
-context find_x
+section find_x
 parameter {p : nat → Prop}
 
 private definition lbp (x : nat) : Prop := ∀ y, y < x → ¬ p y

library/init/funext.lean

@@ -32,7 +32,7 @@ namespace function
   mk_equivalence (@equiv A B) (@equiv.refl A B) (@equiv.symm A B) (@equiv.trans A B)
 end function
 
-context
+section
   open quot
   variables {A : Type} {B : A → Type}
 

library/init/nat.lean

@@ -273,8 +273,8 @@ namespace nat
 
   notation a * b := mul a b
 
-  context
-  attribute sub [reducible]
+  section
+  local attribute sub [reducible]
   definition succ_sub_succ_eq_sub (a b : nat) : succ a - succ b = a - b :=
   nat.induction_on b
     rfl

library/init/prod.lean

@@ -46,10 +46,10 @@ namespace prod
   intro : ∀{a₁ b₁ a₂ b₂}, Ra a₁ a₂ → Rb b₁ b₂ → rprod (a₁, b₁) (a₂, b₂)
   end
 
-  context
+  section
   parameters {A B : Type}
   parameters {Ra  : A → A → Prop} {Rb  : B → B → Prop}
-  infix `≺`:50 := lex Ra Rb
+  local infix `≺`:50 := lex Ra Rb
 
   definition lex.accessible {a} (aca : acc Ra a) (acb : ∀b, acc Rb b): ∀b, acc (lex Ra Rb) (a, b) :=
   acc.rec_on aca

library/init/sigma.lean

@@ -42,10 +42,10 @@ namespace sigma
   | right : ∀a {b₁ b₂},     Rb a b₁ b₂ → lex ⟨a, b₁⟩  ⟨a, b₂⟩
   end
 
-  context
+  section
   parameters {A : Type} {B : A → Type}
   parameters {Ra  : A → A → Prop} {Rb : Π a : A, B a → B a → Prop}
-  infix `≺`:50 := lex Ra Rb
+  local infix `≺`:50 := lex Ra Rb
 
   definition lex.accessible {a} (aca : acc Ra a) (acb : ∀a, well_founded (Rb a)) : ∀ (b : B a), acc (lex Ra Rb) ⟨a, b⟩ :=
   acc.rec_on aca

library/init/wf.lean

@@ -25,9 +25,9 @@ namespace well_founded
   definition apply [coercion] {A : Type} {R : A → A → Prop} (wf : well_founded R) : ∀a, acc R a :=
   take a, well_founded.rec_on wf (λp, p) a
 
-  context
+  section
   parameters {A : Type} {R : A → A → Prop}
-  infix `≺`:50    := R
+  local infix `≺`:50    := R
 
   hypothesis [Hwf : well_founded R]
 
@@ -81,7 +81,7 @@ well_founded.intro (λ (a : A),
 
 -- Subrelation of a well-founded relation is well-founded
 namespace subrelation
-context
+section
   parameters {A : Type} {R Q : A → A → Prop}
   parameters (H₁ : subrelation Q R)
   parameters (H₂ : well_founded R)
@@ -98,7 +98,7 @@ end subrelation
 
 -- The inverse image of a well-founded relation is well-founded
 namespace inv_image
-context
+section
   parameters {A B : Type} {R : B → B → Prop}
   parameters (f : A → B)
   parameters (H : well_founded R)
@@ -119,9 +119,9 @@ end inv_image
 
 -- The transitive closure of a well-founded relation is well-founded
 namespace tc
-context
+section
   parameters {A : Type} {R : A → A → Prop}
-  notation `R⁺` := tc R
+  local notation `R⁺` := tc R
 
   definition accessible {z} (ac: acc R z) : acc R⁺ z :=
   acc.rec_on ac

library/logic/axioms/examples/diaconescu.lean

@@ -8,7 +8,7 @@ open eq.ops nonempty inhabited
 -- Diaconescu’s theorem
 -- Show that Excluded middle follows from
 --   Hilbert's choice operator, function extensionality and Prop extensionality
-context
+section
 parameter  p : Prop
 
 private definition u [reducible] := epsilon (λx, x = true ∨ p)