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_2:110;
then reconsider z = z as Tuple of n,k -SD by A1, FINSEQ_2:110;
take z ; :: thesis: for i being Nat st i in Seg n holds
DigA z,i = SDMinDigit m,k,i
let i be Nat; :: thesis: ( i in Seg n implies DigA z,i = SDMinDigit m,k,i )
assume A4: i in Seg n ; :: thesis: 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; :: thesis: verum