let D be non empty set ; for f, g being FinSequence of D holds g = (ovlpart (f,g)) ^ (ovlrdiff (f,g))
let f, g be FinSequence of D; g = (ovlpart (f,g)) ^ (ovlrdiff (f,g))
ovlpart (f,g) =
smid (g,1,(len (ovlpart (f,g))))
by FINSEQ_8:def 2
.=
g | (len (ovlpart (f,g)))
by FINSEQ_8:5
;
then (ovlpart (f,g)) ^ (ovlrdiff (f,g)) =
(g | (len (ovlpart (f,g)))) ^ (g /^ (len (ovlpart (f,g))))
by FINSEQ_8:def 5
.=
g
by RFINSEQ:8
;
hence
g = (ovlpart (f,g)) ^ (ovlrdiff (f,g))
; verum