let G1 be _Graph; :: thesis: for G2 being G1 -isomorphic _Graph
for G3 being removeLoops of G1
for G4 being removeLoops of G2 holds G4 is G3 -isomorphic
let G2 be G1 -isomorphic _Graph; :: thesis: for G3 being removeLoops of G1
for G4 being removeLoops of G2 holds G4 is G3 -isomorphic
let G3 be removeLoops of G1; :: thesis: for G4 being removeLoops of G2 holds G4 is G3 -isomorphic
let G4 be removeLoops of G2; :: thesis: G4 is G3 -isomorphic
consider F0 being PGraphMapping of G1,G2 such that
A1: F0 is isomorphism by Def23;
reconsider F0 = F0 as one-to-one PGraphMapping of G1,G2 by A1;
consider F being one-to-one PGraphMapping of G3,G4 such that
F = F0 | G3 and
( F0 is weak_SG-embedding implies F is weak_SG-embedding ) and
A2: ( F0 is isomorphism implies F is isomorphism ) and
( F0 is Disomorphism implies F is Disomorphism ) by Th165;
thus G4 is G3 -isomorphic by A1, A2; :: thesis: verum