reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th36:
  for A being Matrix of n,D for p being FinSequence of D, 
      i being Nat st p=A.i & i in Seg n holds len p=n
proof
  let A be Matrix of n,D;
  let p be FinSequence of D, i be Nat;
  assume that
A1: p=A.i and
A2: i in Seg n;
  consider n2 being Nat such that
A3: for x being object st x in rng A ex s being FinSequence of D st s=x &
  len s = n2 by MATRIX_0:9;
  len A=n by MATRIX_0:24;
  then
A4: i in dom A by A2,FINSEQ_1:def 3;
  then A.i in rng A by FUNCT_1:def 3;
  then consider s being FinSequence of D such that
A5: s=A.i and
  len s = n2 by A3;
  s in rng A by A4,A5,FUNCT_1:def 3;
  hence thesis by A1,A5,MATRIX_0:def 2;
end;
