deffunc H₁( Nat) -> Element of k -SD = MminDigit (r,$1);
consider z being FinSequence of k -SD such that
A1: len z = m + 2 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 (m + 2) by A1, FINSEQ_1:def 3;
z is Element of (m + 2) -tuples_on (k -SD) by A1, FINSEQ_2:92;
then reconsider z = z as Tuple of m + 2,k -SD ;
take z ; :: thesis: for i being Nat st i in Seg (m + 2) holds
DigA (z,i) = MminDigit (r,i)
let i be Nat; :: thesis: ( i in Seg (m + 2) implies DigA (z,i) = MminDigit (r,i) )
assume A4: i in Seg (m + 2) ; :: thesis: DigA (z,i) = MminDigit (r,i)
hence DigA (z,i) = z . i by RADIX_1:def 3
.= H₁(i) by A2, A3, A4 ;
:: thesis: verum