deffunc H₁( Point of [:(TOP-REAL 2),(TOP-REAL 2):]) -> Element of REAL = In ((($1 `2) `2),REAL);
consider xo being RealMap of [:(TOP-REAL 2),(TOP-REAL 2):] such that
A10: 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 `2) `2
let x be Point of [:(TOP-REAL 2),(TOP-REAL 2):]; :: thesis: xo . x = (x `2) `2
xo . x = H₁(x) by A10;
hence xo . x = (x `2) `2 ; :: thesis: verum