(** [or A B], written [A \/ B], is the disjunction of [A] and [B] *)

Inductive or (A B:Prop) : Prop :=
  | or_introl : A -> A \/ B
  | or_intror : B -> A \/ B

where "A \/ B" := (or A B) : type_scope.(** [or A B], written [A \/ B], is the disjunction of [A] and [B] *)

Inductive or (A B:Prop) : Prop :=
  | or_introl : A -> A \/ B
  | or_intror : B -> A \/ B

where "A \/ B" := (or A B) : type_scope.(** [or A B], written [A \/ B], is the disjunction of [A] and [B] *)

Inductive or (A B:Prop) : Prop :=
  | or_introl : A -> A \/ B
  | or_intror : B -> A \/ B

where "A \/ B" := (or A B) : type_scope.(** [or A B], written [A \/ B], is the disjunction of [A] and [B] *)

Inductive or (A B:Prop) : Prop :=
  | or_introl : A -> A \/ B
  | or_intror : B -> A \/ B

where "A \/ B" := (or A B) : type_scope.(** [iff A B], written [A <-> B], expresses the equivalence of [A] and [B] *)

Definition iff (A B:Prop) := (A -> B) /\ (B -> A).Notation "A <-> B" := (iff A B) : type_scope.

Theorem not_iff_compat : forall A B : Prop, (A <-> B) -> (~ A <-> ~B).