reserve X for set,
  F for Field_Subset of X,
  M for Measure of F,
  A,B for Subset of X,
  Sets for SetSequence of X,
  seq,seq1,seq2 for ExtREAL_sequence,
  n,k for Nat;
reserve FSets for Set_Sequence of F,
  CA for Covering of A,F;
reserve Cvr for Covering of Sets,F;

theorem Th14:
  C_Meas M is C_Measure of X
proof
  (C_Meas M).{} = 0. by Th11;
  then
A1: C_Meas M is zeroed by VALUED_0:def 19;
  C_Meas M is nonnegative & for A,B being Subset of X st A c= B holds (
C_Meas M ).A <= (C_Meas M).B & for F being sequence of bool X holds (C_Meas
  M).( union rng F) <= SUM((C_Meas M)*F) by Th10,Th12,Th13;
  hence thesis by A1,MEASURE4:def 1;
end;
