exists z
case intro.intro.refl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
semi : semi_confluent R
x w z✝ z : A
red_x_z : refl_trans_clos R z✝ z
⊢ joins R z✝ z
case intro.intro.refl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
semi : semi_confluent R
x w z✝ z : A
red_x_z : refl_trans_clos R z✝ z
⊢ refl_trans_clos R z✝ z ∧ refl_trans_clos R z z