let FT be non empty RelStr ; :: thesis: for A being Subset of FT holds (A `) ^delta = A ^delta
let A be Subset of FT; :: thesis: (A `) ^delta = A ^delta
for x being object holds
( x in (A `) ^delta iff x in A ^delta )

proof

let x be object ; :: thesis: ( x in (A `) ^delta iff x in A ^delta )
thus ( x in (A `) ^delta implies x in A ^delta ) :: thesis: ( x in A ^delta implies x in (A `) ^delta )

proof

assume A1: x in (A `) ^delta ; :: thesis: x in A ^delta
then reconsider y = x as Element of FT ;
( U_FT y meets A ` & U_FT y meets (A `) ` ) by A1, Th5;
hence x in A ^delta ; :: thesis: verum

end;

assume A2: x in A ^delta ; :: thesis: x in (A `) ^delta
then reconsider y = x as Element of FT ;
( U_FT y meets (A `) ` & U_FT y meets A ` ) by A2, Th5;
hence x in (A `) ^delta ; :: thesis: verum

end;

hence (A `) ^delta = A ^delta by TARSKI:2; :: thesis: verum