let r be Real; :: thesis: for p being Point of (TOP-REAL 2) holds
( (r * p) `1 = r * (p `1 ) & (r * p) `2 = r * (p `2 ) )
let p be Point of (TOP-REAL 2); :: thesis: ( (r * p) `1 = r * (p `1 ) & (r * p) `2 = r * (p `2 ) )
r * p = |[(r * (p `1 )),(r * (p `2 ))]| by EUCLID:61;
hence ( (r * p) `1 = r * (p `1 ) & (r * p) `2 = r * (p `2 ) ) by EUCLID:56; :: thesis: verum