File: Mathlib/Algebra/Order/Interval/Set/Monoid.lean

full_name: Set.Ici_add_bij
code: theorem Ici_add_bij : BijOn (· + d) (Ici a) (Ici (a + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Ici a) (Set.Ici (a + d))

full_name: Set.Ioi_add_bij
code: theorem Ioi_add_bij : BijOn (· + d) (Ioi a) (Ioi (a + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Ioi a) (Set.Ioi (a + d))

full_name: Set.Icc_add_bij
code: theorem Icc_add_bij : BijOn (· + d) (Icc a b) (Icc (a + d) (b + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Icc a b) (Set.Icc (a + d) (b + d))

full_name: Set.Ioo_add_bij
code: theorem Ioo_add_bij : BijOn (· + d) (Ioo a b) (Ioo (a + d) (b + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Ioo a b) (Set.Ioo (a + d) (b + d))

full_name: Set.Ioc_add_bij
code: theorem Ioc_add_bij : BijOn (· + d) (Ioc a b) (Ioc (a + d) (b + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Ioc a b) (Set.Ioc (a + d) (b + d))

full_name: Set.Ico_add_bij
code: theorem Ico_add_bij : BijOn (· + d) (Ico a b) (Ico (a + d) (b + d)) 
goal: Set.BijOn (fun x => x + d) (Set.Ico a b) (Set.Ico (a + d) (b + d))

full_name: Set.image_add_const_Ici
code: @[simp]
theorem image_add_const_Ici : (fun x => x + a) '' Ici b = Ici (b + a) 
goal: (fun x => x + a) '' Set.Ici b = Set.Ici (b + a)

full_name: Set.image_add_const_Ioi
code: @[simp]
theorem image_add_const_Ioi : (fun x => x + a) '' Ioi b = Ioi (b + a) 
goal: (fun x => x + a) '' Set.Ioi b = Set.Ioi (b + a)

full_name: Set.image_add_const_Icc
code: @[simp]
theorem image_add_const_Icc : (fun x => x + a) '' Icc b c = Icc (b + a) (c + a) 
goal: (fun x => x + a) '' Set.Icc b c = Set.Icc (b + a) (c + a)

full_name: Set.image_add_const_Ico
code: @[simp]
theorem image_add_const_Ico : (fun x => x + a) '' Ico b c = Ico (b + a) (c + a) 
goal: (fun x => x + a) '' Set.Ico b c = Set.Ico (b + a) (c + a)

full_name: Set.image_add_const_Ioc
code: @[simp]
theorem image_add_const_Ioc : (fun x => x + a) '' Ioc b c = Ioc (b + a) (c + a) 
goal: (fun x => x + a) '' Set.Ioc b c = Set.Ioc (b + a) (c + a)

full_name: Set.image_add_const_Ioo
code: @[simp]
theorem image_add_const_Ioo : (fun x => x + a) '' Ioo b c = Ioo (b + a) (c + a) 
goal: (fun x => x + a) '' Set.Ioo b c = Set.Ioo (b + a) (c + a)

full_name: Set.image_const_add_Ici
code: @[simp]
theorem image_const_add_Ici : (fun x => a + x) '' Ici b = Ici (a + b) 
goal: (fun x => a + x) '' Set.Ici b = Set.Ici (a + b)

full_name: Set.image_const_add_Ioi
code: @[simp]
theorem image_const_add_Ioi : (fun x => a + x) '' Ioi b = Ioi (a + b) 
goal: (fun x => a + x) '' Set.Ioi b = Set.Ioi (a + b)

full_name: Set.image_const_add_Icc
code: @[simp]
theorem image_const_add_Icc : (fun x => a + x) '' Icc b c = Icc (a + b) (a + c) 
goal: (fun x => a + x) '' Set.Icc b c = Set.Icc (a + b) (a + c)

full_name: Set.image_const_add_Ico
code: @[simp]
theorem image_const_add_Ico : (fun x => a + x) '' Ico b c = Ico (a + b) (a + c) 
goal: (fun x => a + x) '' Set.Ico b c = Set.Ico (a + b) (a + c)

full_name: Set.image_const_add_Ioc
code: @[simp]
theorem image_const_add_Ioc : (fun x => a + x) '' Ioc b c = Ioc (a + b) (a + c) 
goal: (fun x => a + x) '' Set.Ioc b c = Set.Ioc (a + b) (a + c)

full_name: Set.image_const_add_Ioo
code: @[simp]
theorem image_const_add_Ioo : (fun x => a + x) '' Ioo b c = Ioo (a + b) (a + c) 
goal: (fun x => a + x) '' Set.Ioo b c = Set.Ioo (a + b) (a + c)