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;

theorem Th7:
 for X be finite binary DecoratedTree of IndexedREAL
 holds LeavesSet({X}) = {Leaves X}
proof
 let X be finite binary DecoratedTree of IndexedREAL;
for x be object holds x in LeavesSet({X}) iff x in {Leaves X}
 proof
 let x be object;
 hereby assume x in LeavesSet({X}); then
 consider p be Element of BinFinTrees IndexedREAL such that
 A1: x = Leaves p & p in {X};
 p = X by A1,TARSKI:def 1;
 hence x in {Leaves X} by TARSKI:def 1,A1;
 end;
 assume x in {Leaves X}; then
 A2: x = Leaves X by TARSKI:def 1;
 dom X is finite & dom X is binary by BINTREE1:def 3; then
 reconsider p= X as Element of BinFinTrees IndexedREAL by Def2;
 p in {X} by TARSKI:def 1;
 hence x in LeavesSet({X}) by A2;
 end;
hence thesis by TARSKI:2;
end;
