reserve n,i,j,k,l for Nat;
reserve D for non empty set;
reserve c,d for Element of D;
reserve p,q,q9,r for FinSequence of D;

theorem
  i in Seg n implies ex j,k st n = j+1+k & i = j+1
proof
  assume
A1: i in Seg(n);
  then 1<=i by FINSEQ_1:1;
  then consider j being Nat such that
A2: i = 1+j by NAT_1:10;
  reconsider j as Element of NAT by ORDINAL1:def 12;
  i<=n by A1,FINSEQ_1:1;
  then consider k being Nat such that
A3: n = j+1+k by A2,NAT_1:10;
  reconsider k as Element of NAT by ORDINAL1:def 12;
  take j,k;
  thus thesis by A2,A3;
end;
