F : Type ?u.24201
α : Type u_2
β : Type u_1
γ : Type ?u.24210
inst✝³ : LinearOrderedField α
inst✝² : ConditionallyCompleteLinearOrderedField β
inst✝¹ : ConditionallyCompleteLinearOrderedField γ
inst✝ : Archimedean α
a : α
b : β
q : ℚ
x y : α
⊢ sSup (cutMap β x + cutMap β y) = inducedMap α β x + inducedMap α β y
F : Type ?u.24201
α : Type u_2
β : Type u_1
γ : Type ?u.24210
inst✝³ : LinearOrderedField α
inst✝² : ConditionallyCompleteLinearOrderedField β
inst✝¹ : ConditionallyCompleteLinearOrderedField γ
inst✝ : Archimedean α
a : α
b : β
q : ℚ
x y : α
⊢ inducedMap α β (x + y) = inducedMap α β x + inducedMap α β y
rw [inducedMap, cutMap_add]
no goals
F : Type ?u.24201
α : Type u_2
β : Type u_1
γ : Type ?u.24210
inst✝³ : LinearOrderedField α
inst✝² : ConditionallyCompleteLinearOrderedField β
inst✝¹ : ConditionallyCompleteLinearOrderedField γ
inst✝ : Archimedean α
a : α
b : β
q : ℚ
x y : α
⊢ sSup (cutMap β x + cutMap β y) = inducedMap α β x + inducedMap α β y
exact csSup_add (cutMap_nonempty β x) (cutMap_bddAbove β x) (cutMap_nonempty β y)
  (cutMap_bddAbove β y)