let V be RealLinearSpace; :: thesis: for x, y, u being VECTOR of V st Gen x,y holds
u = ((pr1 (x,y,u)) * x) + ((pr2 (x,y,u)) * y)
let x, y, u be VECTOR of V; :: thesis: ( Gen x,y implies u = ((pr1 (x,y,u)) * x) + ((pr2 (x,y,u)) * y) )
assume A1: Gen x,y ; :: thesis: u = ((pr1 (x,y,u)) * x) + ((pr2 (x,y,u)) * y)
then ex b being Real st u = ((pr1 (x,y,u)) * x) + (b * y) by GEOMTRAP:def 4;
hence u = ((pr1 (x,y,u)) * x) + ((pr2 (x,y,u)) * y) by A1, GEOMTRAP:def 5; :: thesis: verum