let G2 be locally-finite _Graph; :: thesis: for v, w being Vertex of G2
for e being object
for G1 being addEdge of G2,v,e,w holds
( not v <> w or G1 .minOutDegree() = G2 .minOutDegree() or G1 .minOutDegree() = (v .outDegree()) + 1 )
let v, w be Vertex of G2; :: thesis: for e being object
for G1 being addEdge of G2,v,e,w holds
( not v <> w or G1 .minOutDegree() = G2 .minOutDegree() or G1 .minOutDegree() = (v .outDegree()) + 1 )
let e be object ; :: thesis: for G1 being addEdge of G2,v,e,w holds
( not v <> w or G1 .minOutDegree() = G2 .minOutDegree() or G1 .minOutDegree() = (v .outDegree()) + 1 )
let G1 be addEdge of G2,v,e,w; :: thesis: ( not v <> w or G1 .minOutDegree() = G2 .minOutDegree() or G1 .minOutDegree() = (v .outDegree()) + 1 )
(v .outDegree()) +` 1 = (v .outDegree()) +` 1 ;
hence ( not v <> w or G1 .minOutDegree() = G2 .minOutDegree() or G1 .minOutDegree() = (v .outDegree()) + 1 ) by Th72; :: thesis: verum