cases f
t : Th
f : Form
⊢ t⊨f ↔ f ∈ ↑t
case atom
t : Th
a✝ : ℕ
⊢ t⊨#a✝ ↔ #a✝ ∈ ↑t

case neg
t : Th
a✝ : Form
⊢ t⊨~a✝ ↔ ~a✝ ∈ ↑t

case and
t : Th
a✝¹ a✝ : Form
⊢ t⊨a✝¹&a✝ ↔ a✝¹&a✝ ∈ ↑t

case or
t : Th
a✝¹ a✝ : Form
⊢ t⊨a✝¹¦a✝ ↔ a✝¹¦a✝ ∈ ↑t

case impl
t : Th
a✝¹ a✝ : Form
⊢ t⊨a✝¹⊃a✝ ↔ a✝¹⊃a✝ ∈ ↑t