let G1 be _Graph; :: thesis: for G2 being G1 -Disomorphic _Graph
for G3 being DSimpleGraph of G1
for G4 being DSimpleGraph of G2 holds G4 is G3 -Disomorphic
let G2 be G1 -Disomorphic _Graph; :: thesis: for G3 being DSimpleGraph of G1
for G4 being DSimpleGraph of G2 holds G4 is G3 -Disomorphic
let G3 be DSimpleGraph of G1; :: thesis: for G4 being DSimpleGraph of G2 holds G4 is G3 -Disomorphic
let G4 be DSimpleGraph of G2; :: thesis: G4 is G3 -Disomorphic
set G5 = the removeLoops of G1;
set G6 = the removeLoops of G2;
A1: the removeLoops of G2 is the removeLoops of G1 -Disomorphic by Th167;
( G3 is removeDParallelEdges of the removeLoops of G1 & G4 is removeDParallelEdges of the removeLoops of G2 ) by GLIB_009:122;
hence G4 is G3 -Disomorphic by A1, Th170; :: thesis: verum