let G1 be _Graph; :: thesis: for G2 being removeDParallelEdges of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 & v1 is endvertex holds
v2 is endvertex
let G2 be removeDParallelEdges of G1; :: thesis: for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 & v1 is endvertex holds
v2 is endvertex
let v1 be Vertex of G1; :: thesis: for v2 being Vertex of G2 st v1 = v2 & v1 is endvertex holds
v2 is endvertex
let v2 be Vertex of G2; :: thesis: ( v1 = v2 & v1 is endvertex implies v2 is endvertex )
assume A1: ( v1 = v2 & v1 is endvertex ) ; :: thesis: v2 is endvertex
then A2: ( v2 is endvertex or v2 is isolated ) by GLIB_000:84;
not v1 is isolated by A1;
hence v2 is endvertex by A1, A2, Th112; :: thesis: verum