let D be non empty set ; for CR, r being File of D holds addcr (r,CR) = (ovlldiff (r,CR)) ^ CR
let CR, r be File of D; addcr (r,CR) = (ovlldiff (r,CR)) ^ CR
thus addcr (r,CR) =
ovlcon (r,CR)
by FINSEQ_8:def 11
.=
(ovlldiff (r,CR)) ^ ((ovlpart (r,CR)) ^ (ovlrdiff (r,CR)))
by FINSEQ_8:12
.=
(ovlldiff (r,CR)) ^ CR
by Th31
; verum