simp [he, hf, (show x ≠ f by rintro rfl; exact hf he)]
case pos
α : Type u_1
β : Type u_2
s s₁ s₂ t t' : Set α
f✝ : α → β
f : α
inst✝ : DecidableEq α
S : Set α
hf : f ∉ S
x : α
he : x ∈ S
⊢ f ∈ S ↔ x = f ∨ x ∈ S ∧ x ∉ {x}
no goals