deffunc H_{1}( Point of T) -> Element of the carrier of Y = H . [s,$1];

consider f being Function of the carrier of T, the carrier of Y such that

A1: for x being Element of T holds f . x = H_{1}(x)
from FUNCT_2:sch 4();

take f ; :: thesis: for t being Point of T holds f . t = H . (s,t)

let x be Point of T; :: thesis: f . x = H . (s,x)

thus f . x = H . (s,x) by A1; :: thesis: verum

consider f being Function of the carrier of T, the carrier of Y such that

A1: for x being Element of T holds f . x = H

take f ; :: thesis: for t being Point of T holds f . t = H . (s,t)

let x be Point of T; :: thesis: f . x = H . (s,x)

thus f . x = H . (s,x) by A1; :: thesis: verum