let G2 be _Graph; for v1, v2 being Vertex of G2
for e being object
for G1 being addEdge of G2,v1,e,v2 st G2 is loopless & v1 <> v2 holds
G1 is loopless
let v1, v2 be Vertex of G2; for e being object
for G1 being addEdge of G2,v1,e,v2 st G2 is loopless & v1 <> v2 holds
G1 is loopless
let e be object ; for G1 being addEdge of G2,v1,e,v2 st G2 is loopless & v1 <> v2 holds
G1 is loopless
let G1 be addEdge of G2,v1,e,v2; ( G2 is loopless & v1 <> v2 implies G1 is loopless )
assume that
A1:
G2 is loopless
and
A2:
v1 <> v2
; G1 is loopless