deffunc H₁( Tuple of 2,BOOLEAN) -> Element of BOOLEAN = F₁(($1 . 1),($1 . 2));
consider f being Function of (2 -tuples_on BOOLEAN),BOOLEAN such that
A1: for a being Tuple of 2,BOOLEAN holds f . a = H₁(a) from FUNCT_2:sch 4();

hereby :: thesis: verum

take f = f; :: thesis: for x, y being Element of BOOLEAN holds f . <*x,y*> = F₁(x,y)
let x, y be Element of BOOLEAN ; :: thesis: f . <*x,y*> = F₁(x,y)
reconsider a = <*x,y*> as Tuple of 2,BOOLEAN by FINSEQ_2:101;
thus f . <*x,y*> = F₁((a . 1),(a . 2)) by A1
.= F₁(x,(a . 2))
.= F₁(x,y) ; :: thesis: verum

end;