deffunc H₁( Point of S) -> Element of the carrier of Y = H . [$1,t];
consider f being Function of the carrier of S, the carrier of Y such that
A1: for x being Element of S holds f . x = H₁(x) from FUNCT_2:sch 4();
take f ; :: thesis: for s being Point of S holds f . s = H . (s,t)
let x be Point of S; :: thesis: f . x = H . (x,t)
thus f . x = H . (x,t) by A1; :: thesis: verum