let G2 be _Graph; :: thesis: for v1, e being object
for v2 being Vertex of G2
for G1 being addAdjVertex of G2,v1,e,v2 st not v1 in the_Vertices_of G2 & not e in the_Edges_of G2 holds
not G1 is edgeless
let v1, e be object ; :: thesis: for v2 being Vertex of G2
for G1 being addAdjVertex of G2,v1,e,v2 st not v1 in the_Vertices_of G2 & not e in the_Edges_of G2 holds
not G1 is edgeless
let v2 be Vertex of G2; :: thesis: for G1 being addAdjVertex of G2,v1,e,v2 st not v1 in the_Vertices_of G2 & not e in the_Edges_of G2 holds
not G1 is edgeless
let G1 be addAdjVertex of G2,v1,e,v2; :: thesis: ( not v1 in the_Vertices_of G2 & not e in the_Edges_of G2 implies not G1 is edgeless )
assume ( not v1 in the_Vertices_of G2 & not e in the_Edges_of G2 ) ; :: thesis: not G1 is edgeless
then the_Edges_of G1 = (the_Edges_of G2) \/ {e} by GLIB_006:def 14;
hence not G1 is edgeless ; :: thesis: verum