Section rel_dec_p.
Context {T} {R:T -> T -> Prop} {RD:RelDec R} {RDC:RelDec_Correct RD}.
Definition rel_dec_p (x:T) (y:T) : {R x y} + {~R x y}.
Definition neg_rel_dec_p (x:T) (y:T) : {~R x y} + {R x y}.

Theorem rel_dec_neq_false : forall x y,
~eqt x y -> rel_dec x y = false.