fix(library/data/set/basic.lean, function.lean): fix typos

This commit is contained in:
Jeremy Avigad 2015-05-08 10:43:36 +10:00
parent 0b57f7d00a
commit ba78cc42f9
2 changed files with 3 additions and 3 deletions

View file

@ -54,7 +54,7 @@ theorem mem_univ (x : T) : x ∈ univ := trivial
definition inter [reducible] (a b : set T) : set T := λx, x ∈ a ∧ x ∈ b
notation a ∩ b := inter a b
theorem mem_inter (x : T) (a b : set T) : x ∈ a ∩ b ↔ (x ∈ a ∧ x ∈ b) := !iff.refl
theorem mem_inter (x : T) (a b : set T) : x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b := !iff.refl
theorem inter_self (a : set T) : a ∩ a = a :=
setext (take x, !and_self)
@ -76,7 +76,7 @@ setext (take x, !and.assoc)
definition union [reducible] (a b : set T) : set T := λx, x ∈ a x ∈ b
notation a b := union a b
theorem mem_union (x : T) (a b : set T) : x ∈ a b ↔ (x ∈ a x ∈ b) := !iff.refl
theorem mem_union (x : T) (a b : set T) : x ∈ a b ↔ x ∈ a x ∈ b := !iff.refl
theorem union_self (a : set T) : a a = a :=
setext (take x, !or_self)

View file

@ -41,7 +41,7 @@ theorem in_image {f : X → Y} {a : set X} {x : X} {y : Y}
(H1 : x ∈ a) (H2 : f x = y) : y ∈ f '[a] :=
exists.intro x (and.intro H1 H2)
lemma image_compose (f : Y → X) (g : X → Y) (a : set X) : (f ∘ g) '[a] = f '[g '[a]] :=
lemma image_compose (f : Y → Z) (g : X → Y) (a : set X) : (f ∘ g) '[a] = f '[g '[a]] :=
setext (take z,
iff.intro
(assume Hz : z ∈ (f ∘ g) '[a],