inverseTheorem = [st|
Show: AX2EY2∀x∀y(X2(x,y) ↔ Y2(y,x))
  Show: ∀x∀y(X2(x,y) ↔ \w\v[X2(v,w)](y,x))
    Show: ∀y(X2(a,y) ↔ \w\v[X2(v,w)](y,a))
      Show: X2(a,b) -> \w\v[X2(v,w)](b,a)
        X2(a,b):AS
        \w\v[X2(v,w)](b,a):ABS2 5
      :CD 6
      Show: \w\v[X2(v,w)](b,a)-> X2(a,b)
        \w\v[X2(v,w)](b,a):AS
        X2(a,b):APP2 9
      :CD 10
      X2(a,b) <-> \x_1\x_2[X2(x_2,x_1)](b,a):CB 4 8
    :UD 12
  :UD 3
  EY2∀x∀y(X2(x,y) ↔ Y2(y,x)):EG2 2
:UD2 15|]

adjunctionTheorem = 
inverseTheorem = [st|
Show: AX2EY2∀x∀y(X2(x,y) ↔ Y2(y,x))
  Show: ∀x∀y(X2(x,y) ↔ \w\v[X2(v,w)](y,x))
    Show: ∀y(X2(a,y) ↔ \w\v[X2(v,w)](y,a))
      Show: X2(a,b) -> \w\v[X2(v,w)](b,a)
        X2(a,b):AS
        \w\v[X2(v,w)](b,a):ABS2 5
      :CD 6
      Show: \w\v[X2(v,w)](b,a)-> X2(a,b)
        \w\v[X2(v,w)](b,a):AS
        X2(a,b):APP2 9
      :CD 10
      X2(a,b) <-> \x_1\x_2[X2(x_2,x_1)](b,a):CB 4 8
    :UD 12
  :UD 3
  EY2∀x∀y(X2(x,y) ↔ Y2(y,x)):EG2 2
:UD2 15|]
inverseTheorem = [st|
Show: AX2EY2∀x∀y(X2(x,y) ↔ Y2(y,x))
  Show: ∀x∀y(X2(x,y) ↔ \w\v[X2(v,w)](y,x))
    Show: ∀y(X2(a,y) ↔ \w\v[X2(v,w)](y,a))
      Show: X2(a,b) -> \w\v[X2(v,w)](b,a)
        X2(a,b):AS
        \w\v[X2(v,w)](b,a):ABS2 5
      :CD 6
      Show: \w\v[X2(v,w)](b,a)-> X2(a,b)
        \w\v[X2(v,w)](b,a):AS
        X2(a,b):APP2 9
      :CD 10
      X2(a,b) <-> \x_1\x_2[X2(x_2,x_1)](b,a):CB 4 8
    :UD 12
  :UD 3
  EY2∀x∀y(X2(x,y) ↔ Y2(y,x)):EG2 2
:UD2 15|]