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 Th14:
 for k be Nat
 for s,t be finite binary DecoratedTree of IndexedREAL
 holds union LeavesSet( {s,t} ) = union LeavesSet({MakeTree (t,s,k)})
proof
let k be Nat;
let s,t be finite binary DecoratedTree of IndexedREAL;
A1: {s} \/ {t} = union { {s},{t} } by ZFMISC_1:75
 .= {s,t} by ZFMISC_1:26;
thus union LeavesSet( {s,t} )
 = union (LeavesSet( {s}) \/ LeavesSet( {t}) ) by Th8,A1
 .= union LeavesSet( {s} ) \/ union LeavesSet( {t} ) by ZFMISC_1:78
 .= union { Leaves s } \/ union LeavesSet( {t} ) by Th7
 .= union { Leaves s } \/ union {Leaves t} by Th7
 .= (Leaves s) \/ union {Leaves t} by ZFMISC_1:25
 .= (Leaves s) \/ (Leaves t) by ZFMISC_1:25
 .= Leaves MakeTree (t,s,k) by Th13
 .= union {Leaves MakeTree (t,s,k)} by ZFMISC_1:25
 .= union LeavesSet({MakeTree (t,s,k)}) by Th7;
end;
