let G1 be _Graph; :: thesis: for G2 being SimpleGraph of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
G1 .reachableFrom v1 = G2 .reachableFrom v2
let G2 be SimpleGraph of G1; :: thesis: for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
G1 .reachableFrom v1 = G2 .reachableFrom v2
for W1 being Walk of G1 ex W2 being Walk of G2 st W2 is_Walk_from W1 .first() ,W1 .last() by Th136;
hence for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
G1 .reachableFrom v1 = G2 .reachableFrom v2 by Th35; :: thesis: verum