let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2 st F is isomorphism holds
( G1 is Path-like iff G2 is Path-like )
let F be PGraphMapping of G1,G2; :: thesis: ( F is isomorphism implies ( G1 is Path-like iff G2 is Path-like ) )
assume A1: F is isomorphism ; :: thesis: ( G1 is Path-like iff G2 is Path-like )
then reconsider F0 = F as one-to-one PGraphMapping of G1,G2 ;
F0 " is isomorphism by A1, GLIB_010:75;
hence ( G1 is Path-like implies G2 is Path-like ) by Lm5; :: thesis: ( G2 is Path-like implies G1 is Path-like )
thus ( G2 is Path-like implies G1 is Path-like ) by A1, Lm5; :: thesis: verum