reserve SOURCE for non empty finite set,
 p for Probability of Trivial-SigmaField SOURCE,
 Tseq for FinSequence of BoolBinFinTrees IndexedREAL,
 q for FinSequence of NAT;
reserve T for BinHuffmanTree of p;

theorem
 Leaves T ={ z where z is Element of [:NAT,REAL:]
 :ex x be Element of SOURCE
 st z =[(canFS SOURCE)".x,p.{x}] }
proof
consider Tseq be FinSequence of BoolBinFinTrees IndexedREAL,
 q being FinSequence of NAT such that
A1: Tseq,q,p is_constructingBinHuffmanTree &
 {T} = Tseq.(len Tseq) by Def13;
 1 <= len Tseq by NAT_1:14,A1; then
A2: union LeavesSet({T}) = { z where z is Element of [:NAT,REAL:]
 :ex x be Element of SOURCE st z =[(canFS SOURCE)".x,p.{x}] } by Th19,A1;
 LeavesSet({T}) = {Leaves T } by Th7;
hence thesis by A2,ZFMISC_1:25;
end;
