let AA be SetSequence of REAL; :: thesis: ex A being SetSequence of REAL st
for n being Nat holds A . n = (Partial_Union AA) . n
deffunc H₁( Nat) -> Element of bool REAL = (Partial_Union AA) . $1;
consider f being SetSequence of REAL such that
A1: for d being Element of NAT holds f . d = H₁(d) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = (Partial_Union AA) . n
let n be Nat; :: thesis: f . n = (Partial_Union AA) . n
n in NAT by ORDINAL1:def 12;
hence f . n = (Partial_Union AA) . n by A1; :: thesis: verum