let c be Cardinal; :: thesis: for G1, G2 being _Graph
for F being PGraphMapping of G1,G2 st F is isomorphism holds
( G1 is c -regular iff G2 is c -regular )
let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2 st F is isomorphism holds
( G1 is c -regular iff G2 is c -regular )
let F be PGraphMapping of G1,G2; :: thesis: ( F is isomorphism implies ( G1 is c -regular iff G2 is c -regular ) )
assume A1: F is isomorphism ; :: thesis: ( G1 is c -regular iff G2 is c -regular )
hence ( G1 is c -regular implies G2 is c -regular ) by Lm2; :: thesis: ( G2 is c -regular implies G1 is c -regular )
reconsider F0 = F as one-to-one PGraphMapping of G1,G2 by A1;
F0 " is isomorphism by A1, GLIB_010:75;
hence ( G2 is c -regular implies G1 is c -regular ) by Lm2; :: thesis: verum