let R be weakly-normalizing with_UN_property Relation; for a being set holds nf a,R is_a_normal_form_of a,R
let a be set ; nf a,R is_a_normal_form_of a,R
( a in field R or not a in field R )
;
then A1:
a has_a_normal_form_wrt R
by Def14, Th47;
for b, c being set st b is_a_normal_form_of a,R & c is_a_normal_form_of a,R holds
b = c
by Th54;
hence
nf a,R is_a_normal_form_of a,R
by A1, Def12; verum