deffunc H₅( object ) -> Element of bool [:[:(a . $1),(a . $1):],(a . $1):] = pr1 ((a . $1),(a . $1));
consider f being Function such that
A1: ( dom f = dom a & ( for x being object st x in dom a holds
f . x = H₅(x) ) ) from FUNCT_1:sch 3();
take f ; :: thesis: ( dom f = dom a & ( for i being Element of dom a holds f . i is BinOp of (a . i) ) )
thus dom f = dom a by A1; :: thesis: for i being Element of dom a holds f . i is BinOp of (a . i)
let i be Element of dom a; :: thesis: f . i is BinOp of (a . i)
f . i = pr1 ((a . i),(a . i)) by A1;
hence f . i is BinOp of (a . i) ; :: thesis: verum