theorem Th64: :: GLIB_008:64

for G being _finite _Graph
for H being spanning Subgraph of G ex p being non empty Graph-yielding _finite FinSequence st
( p . 1 == H & p . (len p) = G & len p = ((G .size()) - (H .size())) + 1 & ( for n being Element of dom p st n <= (len p) - 1 holds
ex v1, v2 being Vertex of G ex e being object st
( p . (n + 1) is addEdge of p . n,v1,e,v2 & e in (the_Edges_of G) \ (the_Edges_of (p . n)) & v1 in the_Vertices_of (p . n) & v2 in the_Vertices_of (p . n) ) ) )