let f be XFinSequence; for k2 being Element of NAT holds mid f,0 ,k2 = mid f,1,k2
let k2 be Element of NAT ; mid f,0 ,k2 = mid f,1,k2
reconsider k21 = k2 as Element of NAT ;
A1:
0 -' 1 = 0
by NAT_2:10;
A2:
mid f,0 ,k2 = (f | k21) /^ (0 -' 1)
by Def3;
mid f,1,k2 = f | k21
by Th25;
hence
mid f,0 ,k2 = mid f,1,k2
by A2, A1, Th19; verum