case inl.inl
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : a ≤ b
hcd : c ≤ d
h₁ : a < d
h₂ : c < b
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)

case inl.inr
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : a ≤ b
hcd : d < c
h₁ : a < c
h₂ : d < b
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)

case inr.inl
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : b < a
hcd : c ≤ d
h₁ : b < d
h₂ : c < a
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)

case inr.inr
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : b < a
hcd : d < c
h₁ : b < c
h₂ : d < a
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h₁ : min a b < max c d
h₂ : min c d < max a b
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)
cases' le_or_lt a b with hab hab <;> cases' le_or_lt c d with hcd hcd <;>
  simp only [min_eq_left, min_eq_right, max_eq_left, max_eq_right, min_eq_left_of_lt,
    min_eq_right_of_lt, max_eq_left_of_lt, max_eq_right_of_lt, hab, hcd] at h₁ h₂
no goals
case inl.inr
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : a ≤ b
hcd : d < c
h₁ : a < c
h₂ : d < b
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)

case inr.inl
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : b < a
hcd : c ≤ d
h₁ : b < d
h₂ : c < a
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)

case inr.inr
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : b < a
hcd : d < c
h₁ : b < c
h₂ : d < a
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)
all_goals simp [*, min_eq_left_of_lt, max_eq_left_of_lt, min_eq_right_of_lt, max_eq_right_of_lt]
no goals
case inl.inl
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : a ≤ b
hcd : c ≤ d
h₁ : a < d
h₂ : c < b
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)
exact Icc_union_Icc' h₂.le h₁.le
no goals
case inr.inr
α : Type u_1
β : Type ?u.150639
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
hab : b < a
hcd : d < c
h₁ : b < c
h₂ : d < a
⊢ Icc a b ∪ Icc c d = Icc (min a c) (max b d)
simp [*, min_eq_left_of_lt, max_eq_left_of_lt, min_eq_right_of_lt, max_eq_right_of_lt]