digraph deps {
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  ranksep=0.9;
  node [fontname=Inter, fontsize=9];
  edge [fontname=Inter, fontsize=8, color="#8f9780", fontcolor="#c9d1bb", arrowsize=0.6, penwidth=0.8];
  graph [fontname=Inter, fontsize=12, labelloc=t, fontcolor="#c9d1bb", label=<<B>Theorem dependencies M2, 53 results</B>>];
  close_rec_notin [label="close_rec_notin\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="close_rec_notin theory/Binding.v proved"];
  fvs_lift [label="fvs_lift\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="fvs_lift theory/Binding.v proved"];
  has_red_spec [label="has_red_spec\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="has_red_spec theory/Reduction.v proved"];
  open_rec_occurs_false [label="open_rec_occurs_false\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="open_rec_occurs_false theory/Binding.v proved"];
  steps_complete [label="steps_complete\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="steps_complete theory/Reduction.v proved"];
  steps_sound [label="steps_sound\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="steps_sound theory/Reduction.v proved"];
  steps_sound_red1 [label="steps_sound_red1\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="steps_sound_red1 theory/Reduction.v proved"];
  subst_fvar_other [label="subst_fvar_other\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="subst_fvar_other theory/Binding.v proved"];
  subst_fvar_self [label="subst_fvar_self\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="subst_fvar_self theory/Binding.v proved"];
  zdecs_sound [label="zdecs_sound\\n(M1)", shape=box, style="rounded,dashed,filled", fillcolor="transparent", color="#8f9780", penwidth=0.9, fontcolor="#c9d1bb", tooltip="zdecs_sound theory/Reduction.v proved"];
  Plus_to_Star [label="Plus_to_Star", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Plus_to_Star theory/Closure.v proved"];
  Star_red1_context [label="Star_red1_context", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Star_red1_context theory/Closure.v proved"];
  Star_trans [label="Star_trans", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Star_trans theory/Closure.v proved"];
  red1_star [label="red1_star", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="red1_star theory/Closure.v proved"];
  star_one_trans [label="star_one_trans", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="star_one_trans theory/Closure.v proved"];
  enumerate_check [label="enumerate_check", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="enumerate_check theory/Enumerate.v proved"];
  enumerate_complete [label="enumerate_complete", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="enumerate_complete theory/Enumerate.v proved"];
  enumerate_sound [label="enumerate_sound", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="enumerate_sound theory/Enumerate.v proved"];
  in_comb [label="in_comb", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="in_comb theory/Enumerate.v proved"];
  pow2_pos [label="pow2_pos", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="pow2_pos theory/Enumerate.v proved"];
  size_all_terms [label="size_all_terms", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="size_all_terms theory/Enumerate.v proved"];
  Plus_red1_context [label="Plus_red1_context", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Plus_red1_context theory/Metatheory.v proved"];
  Plus_step_trans [label="Plus_step_trans", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Plus_step_trans theory/Metatheory.v proved"];
  Plus_trans [label="Plus_trans", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="Plus_trans theory/Metatheory.v proved"];
  full_comp_aux [label="full_comp_aux", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="full_comp_aux theory/Metatheory.v proved"];
  fvs_zplug_lift [label="fvs_zplug_lift", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="fvs_zplug_lift theory/Metatheory.v proved"];
  lemma_2_1_fv_preserved [label="lemma_2_1_fv_preserved", shape=box, style="rounded,filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="lemma_2_1_fv_preserved (section 2.1) theory/Metatheory.v proved"];
  lemma_2_2_full_comp [label="lemma_2_2_full_comp", shape=box, style="rounded,filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="lemma_2_2_full_comp (section 2.2) theory/Metatheory.v proved"];
  lemma_2_3_beta_sim [label="lemma_2_3_beta_sim", shape=box, style="rounded,filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="lemma_2_3_beta_sim (section 2.3) theory/Metatheory.v proved"];
  occurs_count_false [label="occurs_count_false", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="occurs_count_false theory/Metatheory.v proved"];
  occurs_count_pos [label="occurs_count_pos", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="occurs_count_pos theory/Metatheory.v proved"];
  occurs_count_zero [label="occurs_count_zero", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="occurs_count_zero theory/Metatheory.v proved"];
  occurs_count_zfill_plug [label="occurs_count_zfill_plug", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="occurs_count_zfill_plug theory/Metatheory.v proved"];
  occurs_lift_self [label="occurs_lift_self", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="occurs_lift_self theory/Metatheory.v proved"];
  open_rec_zplug_lift [label="open_rec_zplug_lift", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_zplug_lift theory/Metatheory.v proved"];
  plug_fv_mono [label="plug_fv_mono", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="plug_fv_mono theory/Metatheory.v proved"];
  red1_root_fv [label="red1_root_fv", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="red1_root_fv theory/Metatheory.v proved"];
  red1r_fv [label="red1r_fv", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="red1r_fv theory/Metatheory.v proved"];
  zdecs_nonempty [label="zdecs_nonempty", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="zdecs_nonempty theory/Metatheory.v proved"];
  check_all_true [label="check_all_true", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="check_all_true theory/Random.v proved"];
  check_term_true [label="check_term_true", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="check_term_true theory/Random.v proved"];
  gen_complete [label="gen_complete", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="gen_complete theory/Random.v proved"];
  gen_fv_preserved [label="gen_fv_preserved", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="gen_fv_preserved theory/Random.v proved"];
  gen_list_length [label="gen_list_length", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="gen_list_length theory/Random.v proved"];
  gen_sound [label="gen_sound", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="gen_sound theory/Random.v proved"];
  close_rec_app [label="close_rec_app", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="close_rec_app theory/Substitution.v proved"];
  close_rec_esub [label="close_rec_esub", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="close_rec_esub theory/Substitution.v proved"];
  close_rec_lam [label="close_rec_lam", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="close_rec_lam theory/Substitution.v proved"];
  open_rec_app [label="open_rec_app", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_app theory/Substitution.v proved"];
  open_rec_esub [label="open_rec_esub", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_esub theory/Substitution.v proved"];
  open_rec_lam [label="open_rec_lam", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_lam theory/Substitution.v proved"];
  open_rec_lc [label="open_rec_lc", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_lc theory/Substitution.v proved"];
  open_rec_lc_atom [label="open_rec_lc_atom", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="open_rec_lc_atom theory/Substitution.v proved"];
  subst_app [label="subst_app", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_app theory/Substitution.v proved"];
  subst_esub [label="subst_esub", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_esub theory/Substitution.v proved"];
  subst_lam [label="subst_lam", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_lam theory/Substitution.v proved"];
  subst_lc_self [label="subst_lc_self", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_lc_self theory/Substitution.v proved"];
  subst_notin [label="subst_notin", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_notin theory/Substitution.v proved"];
  subst_other [label="subst_other", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="subst_other theory/Substitution.v proved"];
  corpus_complete [label="corpus_complete", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="corpus_complete theory/Tests.v proved"];
  corpus_decides [label="corpus_decides", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="corpus_decides theory/Tests.v proved"];
  corpus_fv_preserved [label="corpus_fv_preserved", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="corpus_fv_preserved theory/Tests.v proved"];
  corpus_sound [label="corpus_sound", shape=ellipse, style="filled", fillcolor="transparent", color="#a9b492", penwidth=1.0, fontcolor="#c9d1bb", tooltip="corpus_sound theory/Tests.v proved"];
  in_comb -> size_all_terms;
  pow2_pos -> size_all_terms;
  check_all_true -> enumerate_check;
  steps_sound -> enumerate_sound;
  steps_complete -> enumerate_complete;
  occurs_count_zero -> occurs_count_pos;
  occurs_count_false -> occurs_count_zfill_plug;
  occurs_lift_self -> occurs_count_zfill_plug;
  occurs_lift_self -> open_rec_zplug_lift;
  open_rec_occurs_false -> open_rec_zplug_lift;
  occurs_count_zero -> full_comp_aux;
  occurs_count_zfill_plug -> full_comp_aux;
  open_rec_occurs_false -> full_comp_aux;
  open_rec_zplug_lift -> full_comp_aux;
  zdecs_nonempty -> full_comp_aux;
  zdecs_sound -> full_comp_aux;
  full_comp_aux -> lemma_2_2_full_comp;
  fvs_lift -> fvs_zplug_lift;
  fvs_zplug_lift -> red1_root_fv;
  plug_fv_mono -> red1r_fv;
  red1_root_fv -> red1r_fv;
  red1r_fv -> lemma_2_1_fv_preserved;
  Plus_red1_context -> lemma_2_3_beta_sim;
  lemma_2_2_full_comp -> lemma_2_3_beta_sim;
  has_red_spec -> check_term_true;
  steps_sound_red1 -> check_term_true;
  check_term_true -> check_all_true;
  steps_sound -> gen_sound;
  steps_complete -> gen_complete;
  lemma_2_1_fv_preserved -> gen_fv_preserved;
  steps_sound_red1 -> gen_fv_preserved;
  close_rec_notin -> subst_notin;
  open_rec_occurs_false -> subst_notin;
  subst_fvar_self -> subst_lc_self;
  subst_fvar_other -> subst_other;
  open_rec_lc_atom -> open_rec_lc;
  steps_sound -> corpus_sound;
  steps_complete -> corpus_complete;
  has_red_spec -> corpus_decides;
  lemma_2_1_fv_preserved -> corpus_fv_preserved;
  steps_sound_red1 -> corpus_fv_preserved;
}