deffunc H₁( Point of [:(TOP-REAL 2),(TOP-REAL 2):]) -> Element of REAL = In (((($1 `2) `1) - (o `1)),REAL);
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 = H<sub>1</sub>(x) from FUNCT_2:sch 4();
take xo ; :: thesis: for x being Point of [:(TOP-REAL 2),(TOP-REAL 2):] holds xo . x = ((x `2) `1) - (o `1)
let x be Point of [:(TOP-REAL 2),(TOP-REAL 2):]; :: thesis: xo . x = ((x `2) `1) - (o `1)
xo . x = H<sub>1</sub>(x) by A1;
hence xo . x = ((x `2) `1) - (o `1) ; :: thesis: verum