exists X.a
case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
    refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a