proof compose : (!x:t.A(x) => B(x)) => (!x:t.B(x) => C(x)) => (!x:t.A(x) => C(x))
term  compose : (!x:t.A(x) => B(x)) => (!x:t.B(x) => C(x)) => (!x:t.A(x) => C(x))

proof dea1 : (?x:t.A(x) & B(x)) => (?x:t.A(x)) & (?x:t.B(x))
proof dea2 : ((?x:t.A(x)) & (?x:t.B(x))) => (?x:t.A(x) & B(x)) 

proof dao1 : (!x:t.A(x) | B(x)) => (!x:t.A(x)) | (!x:t.B(x))
proof dao2 : ((!x:t.A(x)) | (!x:t.B(x))) => (!x:t.A(x) | B(x)) 

proof daa1 : (!x:t.A(x) & B(x)) => (!x:t.A(x)) & (!x:t.B(x))
term  daa1 : (!x:t.A(x) & B(x)) => (!x:t.A(x)) & (!x:t.B(x))
proof daa2 : ((!x:t.A(x)) & (!x:t.B(x))) => (!x:t.A(x) & B(x)) 
term  daa2 : ((!x:t.A(x)) & (!x:t.B(x))) => (!x:t.A(x) & B(x)) 

proof deo1 : (?x:t.A(x) | B(x)) => (?x:t.A(x)) | (?x:t.B(x))
term  deo1 : (?x:t.A(x) | B(x)) => (?x:t.A(x)) | (?x:t.B(x))
proof deo2 : ((?x:t.A(x)) | (?x:t.B(x))) => (?x:t.A(x) | B(x)) 
term  deo2 : ((?x:t.A(x)) | (?x:t.B(x))) => (?x:t.A(x) | B(x)) 

proof dm1 : ~(?x:t.A(x)) => !x:t.~A(x)
term  dm1 : ~(?x:t.A(x)) => !x:t.~A(x)
proof dm2 : (!x:t.~A(x)) => ~(?x:t.A(x)) 
term  dm2 : (!x:t.~A(x)) => ~(?x:t.A(x))