let X be ComplexUnitarySpace; :: thesis: for x, y being Point of X st x,y are_orthogonal holds
- x,y are_orthogonal
let x, y be Point of X; :: thesis: ( x,y are_orthogonal implies - x,y are_orthogonal )
assume x,y are_orthogonal ; :: thesis: - x,y are_orthogonal
then - (x .|. y) = - 0 ;
hence - x,y are_orthogonal by Th18; :: thesis: verum