intros x y red
case a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x✝ y✝ : A
a✝ : trans_clos (sym_clos (refl_clos R)) x✝ y✝
⊢ ∀ (x y : A), ?a.R✝ x y → refl_clos (sym_clos R) x y
case a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x✝ y✝ : A
a✝ : trans_clos (sym_clos (refl_clos R)) x✝ y✝
x y : A
red : ?a.R✝ x y
⊢ refl_clos (sym_clos R) x y