set Y = { [E,F] where E, F is Dependency of X : E <= F } ;
{ [E,F] where E, F is Dependency of X : E <= F } c= [:(Dependencies X),(Dependencies X):]
proof
let x be
set ;
:: according to TARSKI:def 3 :: thesis: ( not x in { [E,F] where E, F is Dependency of X : E <= F } or x in [:(Dependencies X),(Dependencies X):] )
assume
x in { [E,F] where E, F is Dependency of X : E <= F }
;
:: thesis: x in [:(Dependencies X),(Dependencies X):]
then consider E,
F being
Dependency of
X such that A1:
x = [E,F]
and
E <= F
;
thus
x in [:(Dependencies X),(Dependencies X):]
by A1, ZFMISC_1:def 2;
:: thesis: verum
end;
hence
{ [P,Q] where P, Q is Dependency of X : P <= Q } is Relation of (Dependencies X)
; :: thesis: verum