let F be PGraphMapping of G1,G2; :: thesis: ( F is continuous implies F is Dcontinuous )
assume A8: F is continuous ; :: thesis: F is Dcontinuous
consider u being Vertex of G1 such that
A9: the_Vertices_of G1 = {u} by GLIB_000:22;

now :: thesis: for e9, v, w being object st v in dom (F _V) & w in dom (F _V) & e9 DJoins (F _V) . v,(F _V) . w,G2 holds
ex e being object st
( e DJoins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 )

let e9, v, w be object ; :: thesis: ( v in dom (F _V) & w in dom (F _V) & e9 DJoins (F _V) . v,(F _V) . w,G2 implies ex e being object st
( e DJoins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 ) )
assume A10: ( v in dom (F _V) & w in dom (F _V) & e9 DJoins (F _V) . v,(F _V) . w,G2 ) ; :: thesis: ex e being object st
( e DJoins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 )
then A11: ( v = u & w = u ) by A9, TARSKI:def 1;
e9 Joins (F _V) . v,(F _V) . w,G2 by A10, GLIB_000:16;
then consider e being object such that
A12: ( e Joins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 ) by A8, A10;
take e = e; :: thesis: ( e DJoins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 )
( e DJoins v,w,G1 or e DJoins w,v,G1 ) by A12, GLIB_000:16;
hence ( e DJoins v,w,G1 & e in dom (F _E) & (F _E) . e = e9 ) by A11, A12; :: thesis: verum

end;

hence F is Dcontinuous ; :: thesis: verum