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 Th59:
  len(p - A) = len p implies A misses rng p
proof
  assume
A1: len(p - A) = len p;
A2: len(p - A) = len p - card(p " A) by Th57;
  assume A meets rng p;
  then p " A <> {} by RELAT_1:138;
  hence thesis by A1,A2;
end;
