deffunc H1( Nat) -> Element of k -SD = SDMinDigit (m,k,$1);
consider z being FinSequence of k -SD such that
A1:
len z = n
and
A2:
for j being Nat st j in dom z holds
z . j = H1(j)
from FINSEQ_2:sch 1();
A3:
dom z = Seg n
by A1, FINSEQ_1:def 3;
z is Element of n -tuples_on (k -SD)
by A1, FINSEQ_2:92;
then reconsider z = z as Tuple of n,k -SD ;
take
z
; for i being Nat st i in Seg n holds
DigA (z,i) = SDMinDigit (m,k,i)
let i be Nat; ( i in Seg n implies DigA (z,i) = SDMinDigit (m,k,i) )
assume A4:
i in Seg n
; DigA (z,i) = SDMinDigit (m,k,i)
then
DigA (z,i) = z . i
by RADIX_1:def 3;
hence
DigA (z,i) = SDMinDigit (m,k,i)
by A2, A3, A4; verum