deffunc H₁( Tuple of 3,BOOLEAN) -> Element of BOOLEAN = F₁(($1 . 1),($1 . 2),($1 . 3));
consider f being Function of (3 -tuples_on BOOLEAN),BOOLEAN such that
A1: for a being Tuple of 3,BOOLEAN holds f . a = H₁(a) from FUNCT_2:sch 4();

hereby :: thesis: verum

take f = f; :: thesis: for x, y, z being Element of BOOLEAN holds f . <*x,y,z*> = F₁(x,y,z)
let x, y, z be Element of BOOLEAN ; :: thesis: f . <*x,y,z*> = F₁(x,y,z)
reconsider a = <*x,y,z*> as Tuple of 3,BOOLEAN by FINSEQ_2:104;
thus f . <*x,y,z*> = F₁((a . 1),(a . 2),(a . 3)) by A1
.= F₁(x,(a . 2),(a . 3)) by FINSEQ_1:45
.= F₁(x,y,(a . 3)) by FINSEQ_1:45
.= F₁(x,y,z) by FINSEQ_1:45 ; :: thesis: verum

end;