deffunc H₁( Point of [:(TOP-REAL 2),(TOP-REAL 2):]) -> Element of REAL = (($1 `1) `2) - (($1 `2) `2);
consider xo being RealMap of [:(TOP-REAL 2),(TOP-REAL 2):] such that
A4: 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) `2) - ((x `2) `2)
thus for x being Point of [:(TOP-REAL 2),(TOP-REAL 2):] holds xo . x = ((x `1) `2) - ((x `2) `2) by A4; :: thesis: verum