reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;
reserve
  B,A,M for BinOp of D,
  F,G for D* -valued FinSequence,
  f for FinSequence of D,
  d,d1,d2 for Element of D;
reserve
  F,G for non-empty non empty FinSequence of D*,
  f for non empty FinSequence of D;
reserve f,g for FinSequence of D,
        a,b,c for set,
        F,F1,F2 for finite set;

theorem Th105:
  for f,g be FinSequence st f^g is with_evenly_repeated_values &
    g is with_evenly_repeated_values holds f is with_evenly_repeated_values
proof
  let f,g be FinSequence such that
A1: f^g is with_evenly_repeated_values &
    g is with_evenly_repeated_values;
  let y;
A2: card ((f^g)"{y}) = card (f"{y})+card (g"{y}) by FINSEQ_3:57;
  card ((f^g)"{y}) is even & card (g"{y}) is even by A1;
  hence thesis by A2;
end;
