
theorem
  for f,g being FinSequence st len g>0 & g is_preposition_of f holds g.1=f.1
proof
  let f,g be FinSequence;
  assume that
A1: len g>0 and
A2: g is_preposition_of f;
A4: len g <=len f by A2,FINSEQ_1:63;
  0+1<=len g by A1,NAT_1:13;
  hence thesis by A2,A4,FINSEQ_6:123;
end;
