α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y) ↔ x = z ∧ y = w ∨ x = w ∧ y = z
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ {x, y} = {z, w} ↔ x = z ∧ y = w ∨ x = w ∧ y = z
simp only [Set.Subset.antisymm_iff, Set.insert_subset, Set.mem_insert_iff, Set.mem_singleton_iff,
  Set.singleton_subset_iff]
case mp
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y) → x = z ∧ y = w ∨ x = w ∧ y = z

case mpr
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ x = z ∧ y = w ∨ x = w ∧ y = z → ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y)
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y) ↔ x = z ∧ y = w ∨ x = w ∧ y = z
constructor
no goals
case mp
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y) → x = z ∧ y = w ∨ x = w ∧ y = z
rintro ⟨⟨rfl | rfl, rfl | rfl⟩, ⟨h₁, h₂⟩⟩ <;> simp [h₁, h₂] at * <;> simp [h₁, h₂]
no goals
case mpr
α : Type u
β : Type v
γ : Type w
ι : Sort x
a b : α
s s₁ s₂ t t₁ t₂ u : Set α
x y z w : α
⊢ x = z ∧ y = w ∨ x = w ∧ y = z → ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧ (z = x ∨ z = y) ∧ (w = x ∨ w = y)
rintro (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩) <;> simp