let x be Real; :: thesis: for p being Point of (TOP-REAL 2) holds x * p = |[(x * (p `1)),(x * (p `2))]|
let p be Point of (TOP-REAL 2); :: thesis: x * p = |[(x * (p `1)),(x * (p `2))]|
( (x * p) `1 = x * (p `1) & (x * p) `2 = x * (p `2) ) by RVSUM_1:44;
hence x * p = |[(x * (p `1)),(x * (p `2))]| by Th25; :: thesis: verum