let x be Real; :: thesis: for n being Element of NAT
for A being non empty closed_interval Subset of REAL st A = [.(x + ((2 * n) * PI)),(x + (((2 * n) + 1) * PI)).] holds
sin is_orthogonal_with cos ,A
let n be Element of NAT ; :: thesis: for A being non empty closed_interval Subset of REAL st A = [.(x + ((2 * n) * PI)),(x + (((2 * n) + 1) * PI)).] holds
sin is_orthogonal_with cos ,A
let A be non empty closed_interval Subset of REAL; :: thesis: ( A = [.(x + ((2 * n) * PI)),(x + (((2 * n) + 1) * PI)).] implies sin is_orthogonal_with cos ,A )
assume A = [.(x + ((2 * n) * PI)),(x + (((2 * n) + 1) * PI)).] ; :: thesis: sin is_orthogonal_with cos ,A
then |||(sin,cos,A)||| = 0 by INTEGRA8:96;
hence sin is_orthogonal_with cos ,A by Def2; :: thesis: verum