let C be non empty set ; for f, g being Membership_Func of C holds f \ (min (f,g)) c=
let f, g be Membership_Func of C; f \ (min (f,g)) c=
f \ (min (f,g)) =
min (f,(max ((1_minus f),(1_minus g))))
by FUZZY_1:11
.=
max ((min (f,(1_minus f))),(f \ g))
by FUZZY_1:9
;
hence
f \ (min (f,g)) c=
by FUZZY_1:17; verum