let C1, C2 be non empty set ; ( 1_minus (Zmf (C1,C2)) = Umf (C1,C2) & 1_minus (Umf (C1,C2)) = Zmf (C1,C2) )
A1:
Umf (C1,C2) = UMF [:C1,C2:]
;
Zmf (C1,C2) = EMF [:C1,C2:]
;
hence
( 1_minus (Zmf (C1,C2)) = Umf (C1,C2) & 1_minus (Umf (C1,C2)) = Zmf (C1,C2) )
by A1, FUZZY_1:40; verum