deffunc H_{1}( Tuple of 2,BOOLEAN) -> Element of BOOLEAN = F_{1}(($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 = H_{1}(a)
from FUNCT_2:sch 4();

consider f being Function of (2 -tuples_on BOOLEAN),BOOLEAN such that

A1: for a being Tuple of 2,BOOLEAN holds f . a = H

hereby :: thesis: verum

take f = f; :: thesis: for x, y being Element of BOOLEAN holds f . <*x,y*> = F_{1}(x,y)

let x, y be Element of BOOLEAN ; :: thesis: f . <*x,y*> = F_{1}(x,y)

reconsider a = <*x,y*> as Tuple of 2,BOOLEAN by FINSEQ_2:101;

thus f . <*x,y*> = F_{1}((a . 1),(a . 2))
by A1

.= F_{1}(x,(a . 2))
by FINSEQ_1:44

.= F_{1}(x,y)
by FINSEQ_1:44
; :: thesis: verum

end;let x, y be Element of BOOLEAN ; :: thesis: f . <*x,y*> = F

reconsider a = <*x,y*> as Tuple of 2,BOOLEAN by FINSEQ_2:101;

thus f . <*x,y*> = F

.= F

.= F