[STATEMENT]
lemma hom_graph_compl:
  "hom_graph f S x a \<Longrightarrow> hom_graph f S (- x) (- a)"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. hom_graph f S x a \<Longrightarrow> hom_graph f S (- x) (- a)
[PROOF STEP]
by (induct set: hom_graph, simp_all add: hom_graph.intros compl_ifte)