α : Type u_1
inst✝ : LinearOrderedField α
a✝ a : α
h : 0 < a
b c d : α
⊢ (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b)
α : Type u_1
inst✝ : LinearOrderedField α
a✝ a : α
h : 0 < a
b c d : α
⊢ (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b)
suffices (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b) by
  rwa [Set.image_image] at this
no goals
α : Type u_1
inst✝ : LinearOrderedField α
a✝ a : α
h : 0 < a
b c d : α
⊢ (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b)
rw [image_mul_left_Icc' h, image_add_const_Icc]
no goals
α : Type u_1
inst✝ : LinearOrderedField α
a✝ a : α
h : 0 < a
b c d : α
this : (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b)
⊢ (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b)
rwa [Set.image_image] at this