// This prints the left floatting menu
Dedukti    Load Matita      Load Coq         Load Lean        Load PVS         Load OpenTheory Load
Dedukti-jumb

Axiom

relations.commutative

Statement

λf. ∀ x y, (f x y) = (f y x)

Main Dependencies
constant
logic.eq
Theory
constant
logic.eq
Coq-Jumb
Statement

Definition commutative : forall (A:Type), (A -> A -> A) -> Prop := fun (A:Type) => fun (f:(A -> A -> A)) => forall (x:A), forall (y:A), logic.eq (A) (f x y) (f y x)


Matita-Jumb
Statement

definition commutative : \forall A : Type[0] . (A -> A -> A) -> Prop := \lambda A : Type[0]. \lambda f : A -> A -> A. \forall (x:A). \forall (y:A). (eq) (A) (f x y) (f y x)


Lean-jumb
Statement

def commutative : forall (A : Type) , ((A) -> (A) -> A) -> Prop := fun (A : Type) , fun (f : (A) -> (A) -> A) , forall (x:A) , forall (y:A) , (((logic.eq_) (A)) (((f) (x)) (y))) (((f) (y)) (x))


PVS-jumb
Statement

commutative [A:TYPE+] : [[A -> [A -> A]] -> bool] = (LAMBDA(f:[A -> [A -> A]]):(FORALL(x:A):(FORALL(y:A):logic_sttfa_th.eq[A](f(x)(y))(f(y)(x)))))


OpenTheory

Printing for OpenTheory is not working at the moment.