File: Mathlib/Algebra/Order/Interval/Finset.lean

full_name: Finset.map_add_left_Icc
code: @[simp] lemma map_add_left_Icc (a b c : α) :
    (Icc a b).map (addLeftEmbedding c) = Icc (c + a) (c + b) 
goal: Finset.map (addLeftEmbedding c) (Finset.Icc a b) = Finset.Icc (c + a) (c + b)

full_name: Finset.map_add_right_Icc
code: @[simp] lemma map_add_right_Icc (a b c : α) :
    (Icc a b).map (addRightEmbedding c) = Icc (a + c) (b + c) 
goal: Finset.map (addRightEmbedding c) (Finset.Icc a b) = Finset.Icc (a + c) (b + c)

full_name: Finset.map_add_left_Ico
code: @[simp] lemma map_add_left_Ico (a b c : α) :
    (Ico a b).map (addLeftEmbedding c) = Ico (c + a) (c + b) 
goal: Finset.map (addLeftEmbedding c) (Finset.Ico a b) = Finset.Ico (c + a) (c + b)

full_name: Finset.map_add_right_Ico
code: @[simp] lemma map_add_right_Ico (a b c : α) :
    (Ico a b).map (addRightEmbedding c) = Ico (a + c) (b + c) 
goal: Finset.map (addRightEmbedding c) (Finset.Ico a b) = Finset.Ico (a + c) (b + c)

full_name: Finset.map_add_left_Ioc
code: @[simp] lemma map_add_left_Ioc (a b c : α) :
    (Ioc a b).map (addLeftEmbedding c) = Ioc (c + a) (c + b) 
goal: Finset.map (addLeftEmbedding c) (Finset.Ioc a b) = Finset.Ioc (c + a) (c + b)

full_name: Finset.map_add_right_Ioc
code: @[simp] lemma map_add_right_Ioc (a b c : α) :
    (Ioc a b).map (addRightEmbedding c) = Ioc (a + c) (b + c) 
goal: Finset.map (addRightEmbedding c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)

full_name: Finset.map_add_left_Ioo
code: @[simp] lemma map_add_left_Ioo (a b c : α) :
    (Ioo a b).map (addLeftEmbedding c) = Ioo (c + a) (c + b) 
goal: Finset.map (addLeftEmbedding c) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)

full_name: Finset.map_add_right_Ioo
code: @[simp] lemma map_add_right_Ioo (a b c : α) :
    (Ioo a b).map (addRightEmbedding c) = Ioo (a + c) (b + c) 
goal: Finset.map (addRightEmbedding c) (Finset.Ioo a b) = Finset.Ioo (a + c) (b + c)

full_name: Finset.image_add_left_Icc
code: @[simp] lemma image_add_left_Icc (a b c : α) : (Icc a b).image (c + ·) = Icc (c + a) (c + b) 
goal: Finset.image (fun x => c + x) (Finset.Icc a b) = Finset.Icc (c + a) (c + b)

full_name: Finset.image_add_left_Ico
code: @[simp] lemma image_add_left_Ico (a b c : α) : (Ico a b).image (c + ·) = Ico (c + a) (c + b) 
goal: Finset.image (fun x => c + x) (Finset.Ico a b) = Finset.Ico (c + a) (c + b)

full_name: Finset.image_add_left_Ioc
code: @[simp] lemma image_add_left_Ioc (a b c : α) : (Ioc a b).image (c + ·) = Ioc (c + a) (c + b) 
goal: Finset.image (fun x => c + x) (Finset.Ioc a b) = Finset.Ioc (c + a) (c + b)

full_name: Finset.image_add_left_Ioo
code: @[simp] lemma image_add_left_Ioo (a b c : α) : (Ioo a b).image (c + ·) = Ioo (c + a) (c + b) 
goal: Finset.image (fun x => c + x) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)

full_name: Finset.image_add_right_Icc
code: @[simp] lemma image_add_right_Icc (a b c : α) : (Icc a b).image (· + c) = Icc (a + c) (b + c) 
goal: Finset.image (fun x => x + c) (Finset.Icc a b) = Finset.Icc (a + c) (b + c)

full_name: Finset.image_add_right_Ico
code: @[simp] lemma image_add_right_Ico (a b c : α) : (Ico a b).image (· + c) = Ico (a + c) (b + c) 
goal: Finset.image (fun x => x + c) (Finset.Ico a b) = Finset.Ico (a + c) (b + c)

full_name: Finset.image_add_right_Ioc
code: @[simp] lemma image_add_right_Ioc (a b c : α) : (Ioc a b).image (· + c) = Ioc (a + c) (b + c) 
goal: Finset.image (fun x => x + c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)

full_name: Finset.image_add_right_Ioo
code: @[simp] lemma image_add_right_Ioo (a b c : α) : (Ioo a b).image (· + c) = Ioo (a + c) (b + c) 
goal: Finset.image (fun x => x + c) (Finset.Ioo a b) = Finset.Ioo (a + c) (b + c)