reserve k,m,n for Nat,
  a, b, c for object,
  x, y, X, Y, Z for set,
  D for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R, P1, P2, Q1, Q2, R1, R2 for FinSequence-membered set;
reserve S, T for non empty FinSequence-membered set;
reserve A for Function of P, NAT;
reserve U, V, W for Subset of P*;

theorem Th29:
  for X being set for B being disjoint_valued FinSequence of bool X
    for a, b, c st a in B.b & a in B.c holds b = c & b in dom B
proof
  let X be set, B be disjoint_valued FinSequence of bool X,
  a, b, c;
  assume that A1: a in B.b and A2: a in B.c;
  A3: b in dom B by A1, FUNCT_1:def 2;
  A4: c in dom B by A2, FUNCT_1:def 2;
  B.b meets B.c by A1, A2, XBOOLE_0:def 4;
  hence thesis by A3, A4, Def13;
end;
