set V = {0,1};
set E = {0};
set S = 0 .--> 0;
set T = 0 .--> 1;
A7: dom (0 .--> 1) = {0} ;

A8: now :: thesis: for x being object st x in {0} holds
(0 .--> 1) . x in {0,1}

let x be object ; :: thesis: ( x in {0} implies (0 .--> 1) . x in {0,1} )
assume x in {0} ; :: thesis: (0 .--> 1) . x in {0,1}
then x = 0 by TARSKI:def 1;
then (0 .--> 1) . x = 1 by FUNCOP_1:72;
hence (0 .--> 1) . x in {0,1} by TARSKI:def 2; :: thesis: verum

end;

A9: now :: thesis: for x being object st x in {0} holds
(0 .--> 0) . x in {0,1}

let x be object ; :: thesis: ( x in {0} implies (0 .--> 0) . x in {0,1} )
assume x in {0} ; :: thesis: (0 .--> 0) . x in {0,1}
then x = 0 by TARSKI:def 1;
then (0 .--> 0) . x = 0 by FUNCOP_1:72;
hence (0 .--> 0) . x in {0,1} by TARSKI:def 2; :: thesis: verum

end;

reconsider T = 0 .--> 1 as Function of {0},{0,1} by A7, A8, FUNCT_2:3;
dom (0 .--> 0) = {0} ;
then reconsider S = 0 .--> 0 as Function of {0},{0,1} by A9, FUNCT_2:3;
set G = createGraph ({0,1},{0},S,T);
take createGraph ({0,1},{0},S,T) ; :: thesis: ( not createGraph ({0,1},{0},S,T) is _trivial & createGraph ({0,1},{0},S,T) is _finite & createGraph ({0,1},{0},S,T) is simple & createGraph ({0,1},{0},S,T) is chordal )
A10: (the_Source_of (createGraph ({0,1},{0},S,T))) . 0 = 0 by FUNCOP_1:72;

now :: thesis: not card (the_Vertices_of (createGraph ({0,1},{0},S,T))) = 1

assume card (the_Vertices_of (createGraph ({0,1},{0},S,T))) = 1 ; :: thesis: contradiction
then ex x being object st the_Vertices_of (createGraph ({0,1},{0},S,T)) = {x} by CARD_2:42;
hence contradiction by ZFMISC_1:5; :: thesis: verum

end;

hence ( not createGraph ({0,1},{0},S,T) is _trivial & createGraph ({0,1},{0},S,T) is _finite ) ; :: thesis: ( createGraph ({0,1},{0},S,T) is simple & createGraph ({0,1},{0},S,T) is chordal )
A12: (the_Target_of (createGraph ({0,1},{0},S,T))) . 0 = 1 by FUNCOP_1:72;
0 in the_Edges_of (createGraph ({0,1},{0},S,T)) by TARSKI:def 1;
then A14: 0 Joins 0 ,1, createGraph ({0,1},{0},S,T) by A10, A12;

now :: thesis: for v, e being object holds not e Joins v,v, createGraph ({0,1},{0},S,T)

let v, e be object ; :: thesis: not e Joins v,v, createGraph ({0,1},{0},S,T)
assume A15: e Joins v,v, createGraph ({0,1},{0},S,T) ; :: thesis: contradiction
reconsider v = v as Vertex of (createGraph ({0,1},{0},S,T)) by A15, GLIB_000:13;
e in the_Edges_of (createGraph ({0,1},{0},S,T)) by A15;
then e Joins 0 ,1, createGraph ({0,1},{0},S,T) by A14, TARSKI:def 1;
then ( ( 0 = v & 1 = v ) or ( 0 = v & 1 = v ) ) by A15;
hence contradiction ; :: thesis: verum

end;

then A16: createGraph ({0,1},{0},S,T) is loopless by GLIB_000:18;

now :: thesis: for e1, e2, v1, v2 being object st e1 Joins v1,v2, createGraph ({0,1},{0},S,T) & e2 Joins v1,v2, createGraph ({0,1},{0},S,T) holds
not e1 <> e2

let e1, e2, v1, v2 be object ; :: thesis: ( e1 Joins v1,v2, createGraph ({0,1},{0},S,T) & e2 Joins v1,v2, createGraph ({0,1},{0},S,T) implies not e1 <> e2 )
assume that
A17: e1 Joins v1,v2, createGraph ({0,1},{0},S,T) and
A18: e2 Joins v1,v2, createGraph ({0,1},{0},S,T) ; :: thesis: not e1 <> e2
e1 in {0} by A17;
then A19: e1 = 0 by TARSKI:def 1;
assume A20: e1 <> e2 ; :: thesis: contradiction
e2 in {0} by A18;
hence contradiction by A20, A19, TARSKI:def 1; :: thesis: verum

end;

then createGraph ({0,1},{0},S,T) is non-multi ;
hence createGraph ({0,1},{0},S,T) is simple by A16; :: thesis: createGraph ({0,1},{0},S,T) is chordal
card (the_Vertices_of (createGraph ({0,1},{0},S,T))) = 2 by CARD_2:57;
hence createGraph ({0,1},{0},S,T) is chordal by Th95; :: thesis: verum