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

hereby :: thesis: verum

take f = f; :: thesis: for x being Element of BOOLEAN holds f . <*x*> = F₁(x)
let x be Element of BOOLEAN ; :: thesis: f . <*x*> = F₁(x)
reconsider a = <*x*> as Element of 1 -tuples_on BOOLEAN by FINSEQ_2:98;
thus f . <*x*> = F₁((a . 1)) by A1
.= F₁(x) ; :: thesis: verum

end;