let n be Element of NAT ; :: thesis: for A being closed-interval Subset of REAL st A = [.((2 * n) * PI ),(((2 * n) + 1) * PI ).] holds
sin is_orthogonal_with cos ,A
let A be closed-interval Subset of REAL ; :: thesis: ( A = [.((2 * n) * PI ),(((2 * n) + 1) * PI ).] implies sin is_orthogonal_with cos ,A )
assume A = [.((2 * n) * PI ),(((2 * n) + 1) * PI ).] ; :: thesis: sin is_orthogonal_with cos ,A
then |||(sin ,cos ,A)||| = 0 by INTEGRA8:95;
hence sin is_orthogonal_with cos ,A by Def2; :: thesis: verum