deffunc H₁( Point of [:(TOP-REAL 2),(TOP-REAL 2):]) -> Element of REAL = (($1 `1) `1) - (($1 `2) `1);
consider xo being RealMap of [:(TOP-REAL 2),(TOP-REAL 2):] such that
A1: for x being Point of [:(TOP-REAL 2),(TOP-REAL 2):] holds xo . x = H₁(x) from FUNCT_2:sch 4();
take xo ; :: thesis: for x being Point of [:(TOP-REAL 2),(TOP-REAL 2):] holds xo . x = ((x `1) `1) - ((x `2) `1)
thus for x being Point of [:(TOP-REAL 2),(TOP-REAL 2):] holds xo . x = ((x `1) `1) - ((x `2) `1) by A1; :: thesis: verum