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
for X be non empty finite Subset of BinFinTrees IndexedREAL,
p be Element of BinFinTrees IndexedREAL
st p in X holds Vrootl p <= MaxVl(X)
proof
let X be non empty finite Subset of BinFinTrees IndexedREAL,
p be Element of BinFinTrees IndexedREAL;
assume A1: p in X;
 consider L be non empty finite Subset of NAT such that A2:
L = {Vrootl p where p is Element of BinFinTrees IndexedREAL: p in X }
 & MaxVl X = max L by Def9;
Vrootl p in L by A2,A1;
hence thesis by XXREAL_2:def 8,A2;
end;
