let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2
for v being Vertex of G1 st F is onto & F is semi-Dcontinuous & v in dom (F _V) holds
((F _V) /. v) .degree() c= v .degree()
let F be PGraphMapping of G1,G2; :: thesis: for v being Vertex of G1 st F is onto & F is semi-Dcontinuous & v in dom (F _V) holds
((F _V) /. v) .degree() c= v .degree()
let v be Vertex of G1; :: thesis: ( F is onto & F is semi-Dcontinuous & v in dom (F _V) implies ((F _V) /. v) .degree() c= v .degree() )
assume ( F is onto & F is semi-Dcontinuous & v in dom (F _V) ) ; :: thesis: ((F _V) /. v) .degree() c= v .degree()
then ( ((F _V) /. v) .inDegree() c= v .inDegree() & ((F _V) /. v) .outDegree() c= v .outDegree() ) by Th96;
hence ((F _V) /. v) .degree() c= v .degree() by CARD_2:83; :: thesis: verum