The Formalization of Discrete Fourier Transform in HOL

Algorithm 3

The formalization of EULER_COS.

val EULER_COS = store_thm(“EULER_COS”,

“ n:real. (cos n,0) = (1)/(2) (exp (i n) + exp (i (-n)))”,

GEN_TAC THEN REWRITE_TAC [EXP_IMAGINARY] THEN

REWRITE_TAC [complex_add, RE, IM, FST, SND] THEN

REWRITE_TAC [COS_NEG, SIN_NEG] THEN

SRW_TAC [REAL_DOUBLE] THEN

REWRITE_TAC [complex_scalar_lmul, RE, IM, FST, SND]

THEN SRW_TAC [REAL_MUL_ASSOC])