let f, g be FinSequence; ( len f >= 1 implies mid ((f ^ g),1,(len f)) = f )
assume A1:
len f >= 1
; mid ((f ^ g),1,(len f)) = f
then
(len f) - 1 >= 0
by XREAL_1:48;
then
(len f) - 1 = (len f) -' 1
by XREAL_0:def 2;
then A2:
((len f) -' 1) + 1 = len f
;
1 - 1 = 0
;
then A3:
1 -' 1 = 0
by XREAL_0:def 2;
(f ^ g) | (len f) = f
by FINSEQ_5:23;
then
((f ^ g) /^ 0) | (len f) = f
by FINSEQ_5:28;
hence
mid ((f ^ g),1,(len f)) = f
by A1, A2, A3, FINSEQ_6:def 3; verum