reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th25:
  n in dom p iff 1 <= n & n <= len p
proof
  thus n in dom p implies 1 <= n & n <= len p
  proof
    assume n in dom p;
    then n in Seg(len p) by FINSEQ_1:def 3;
    hence thesis by FINSEQ_1:1;
  end;
  assume that
A1: 1 <= n and
A2: n <= len p;
  n in Seg(len p) by A1,A2,FINSEQ_1:1;
  hence thesis by FINSEQ_1:def 3;
end;
