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))