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R_Gc_disjoint [label="R_Gc_disjoint", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="R_Gc_disjoint theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
Star_red_sub_context [label="Star_red_sub_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Star_red_sub_context theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
full_comp_aux_sub [label="full_comp_aux_sub", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="full_comp_aux_sub theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
plus_red_sub_full_comp [label="plus_red_sub_full_comp", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="plus_red_sub_full_comp theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
star_red_sub_full_comp [label="star_red_sub_full_comp", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="star_red_sub_full_comp theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
es_count_plug_mono [label="es_count_plug_mono", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="es_count_plug_mono theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
red_gc_measure [label="red_gc_measure", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_gc_measure theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
red_gc_terminates [label="red_gc_terminates", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_gc_terminates theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
red_gc_to_red_sub [label="red_gc_to_red_sub", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_gc_to_red_sub theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
corpus_sound [label="corpus_sound", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="corpus_sound theory/Tests.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
corpus_complete [label="corpus_complete", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="corpus_complete theory/Tests.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
corpus_decides [label="corpus_decides", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="corpus_decides theory/Tests.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
corpus_fv_preserved [label="corpus_fv_preserved", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="corpus_fv_preserved theory/Tests.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
lift_lc -> lift_0_lc;
fvs_lift -> open_rec_fvs;
open_rec_bvar -> open_rec_fvs;
open_rec_bvar_neq -> open_rec_fvs;
open_rec_bvar -> open_close;
lift_0_lc -> subst_fvar_self;
close_rec_fvs -> subst_fvs;
open_rec_fvs -> subst_fvs;
in_comb -> size_all_terms;
pow2_pos -> size_all_terms;
check_all_true -> enumerate_check;
steps_sound -> enumerate_sound;
steps_complete -> enumerate_complete;
of_trm_lift -> of_trm_open;
mfvs_lift_m -> mfvs_open_m;
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;
par_red1_iff -> par_to_red1_or_eq;
par_red1_iff -> red1_or_eq_to_par;
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;
zdecs_sound -> root_steps_sound;
zdecs_complete -> root_steps_complete;
positions_at -> steps_sound;
root_steps_sound -> steps_sound;
steps_sound -> steps_sound_red1;
positions_hole -> root_steps_in_steps;
at_ctx_comp -> steps_complete;
plug_comp -> steps_complete;
positions_comp -> steps_complete;
root_steps_complete -> steps_complete;
root_steps_in_steps -> steps_complete;
has_red_f -> has_red_spec;
steps_complete -> has_red_spec;
steps_sound -> has_red_spec;
has_red_spec -> red1_dec;
steps_complete -> nf_iff_steps_nil;
steps_sound_red1 -> nf_iff_steps_nil;
nf_iff_steps_nil -> normal_form_iff_nf;
nf_iff_steps_nil -> nf_dec;
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;
red_sub_root_to_red1 -> red_sub_to_red1;
occurs_zfill -> zfill_occurs0;
zfill_occurs0 -> R_Gc_disjoint;
red_sub_context -> Star_red_sub_context;
occurs_count_zero -> full_comp_aux_sub;
occurs_count_zfill_plug -> full_comp_aux_sub;
open_rec_occurs_false -> full_comp_aux_sub;
open_rec_zplug_lift -> full_comp_aux_sub;
red_sub_gc -> full_comp_aux_sub;
red_sub_r -> full_comp_aux_sub;
zdecs_nonempty -> full_comp_aux_sub;
zdecs_sound -> full_comp_aux_sub;
full_comp_aux_sub -> plus_red_sub_full_comp;
Plus_to_Star -> star_red_sub_full_comp;
plus_red_sub_full_comp -> star_red_sub_full_comp;
es_count_plug_mono -> red_gc_measure;
red_gc_measure -> red_gc_terminates;
red_sub_gc -> red_gc_to_red_sub;
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;
}