reserve Omega for set;
reserve m,n,k for Nat;
reserve x,y for object;
reserve r,r1,r2,r3 for Real;
reserve seq,seq1 for Real_Sequence;
reserve Sigma for SigmaField of Omega;
reserve ASeq,BSeq for SetSequence of Sigma;
reserve A, B, C, A1, A2, A3 for Event of Sigma;
reserve Omega for non empty set;
reserve Sigma for SigmaField of Omega;
reserve A, B, C, A1, A2, A3 for Event of Sigma;
reserve ASeq,BSeq for SetSequence of Sigma;
reserve P,P1,P2 for Probability of Sigma;

theorem Th36:
  for A,B,P st 0 < P.A & 0 < P.B holds P.|.B.A = P.|.A.B * P.A / P .B
proof
  let A,B,P;
  assume that
A1: 0 < P.A and
A2: 0 < P.B;
  thus P.|.A.B * P.A / P.B = P.(A /\ B) / P.B by A1,Th29
    .= P.|.B.A by A2,Def6;
end;
