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 Th16:
 for x be object, D be non empty set,
 T be finite binary DecoratedTree of D st T = root-tree x holds
 Leaves (T) = {x}
proof
 let x be object, D be non empty set,
 T be finite binary DecoratedTree of D;
 assume A1: T = root-tree x;
 A2: {} in elementary_tree 0 by TARSKI:def 1,TREES_1:29; then
 A3: T.{} = x by A1,FUNCOP_1:7;
 A4: dom T = elementary_tree 0 by A1;
 A5: Leaves dom T = {{}} by TREES_1:29,Th15,A1;
thus Leaves (T) = Im (T,{}) by RELAT_1:def 16,A5
 .={x} by A3,A4,A2,FUNCT_1:59;
end;
