diff --git a/RingMult b/RingMult deleted file mode 100644 index 537eb43..0000000 --- a/RingMult +++ /dev/null @@ -1,24 +0,0 @@ - Record int_bipart : Set := {pneg : nat; ppos : nat}. - - - - Notation "a !+ b" := (Peano.plus a b) (at level 50, left associativity). - Definition plus a b := Build_int_bipart - (pneg a !+ pneg b) (ppos a !+ ppos b). - Notation "a + b" := (plus a b). - -Definition int_bipart_eq_part - : forall an bn, an = bn -> forall ap bp, ap = bp - -> Build_int_bipart an ap = Build_int_bipart bn bp. - Proof. - refine (fun _ _ eqn _ _ eqp => _). - refine (eq_ind _ (fun n => _ = Build_int_bipart n _) _ _ eqn). - refine (f_equal _ eqp). - Qed. - - Require Import ArithRing. - - Definition mult_comm : forall n m, n * m = m * n. - Proof. - refine (fun n m => int_bipart_eq_part _ _ _ _ _ _); simpl; ring. - Qed.