156 lines
20 KiB
Plaintext
156 lines
20 KiB
Plaintext
digraph theorem_deps {
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rankdir=LR;
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bgcolor="white";
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splines=spline;
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nodesep=0.22;
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ranksep=0.6;
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node [fontname=Inter, fontsize=9, fontcolor="#222222"];
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edge [fontname=Inter, fontsize=8, color="#9a9a9a", arrowsize=0.6, penwidth=0.8];
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graph [fontname=Inter, fontsize=12, labelloc=t, label=<<B>Milner's Lambda-Calculus with Partial Substitutions - theorem dependency (M2)</B><BR/><FONT POINT-SIZE="9"><FONT COLOR="#38761d">proved</FONT> <FONT COLOR="#b45f06">stated</FONT> <FONT COLOR="#777777">planned</FONT> <FONT COLOR="#cc0000">blocked</FONT></FONT>>];
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fvs_lift [label="fvs_lift", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="fvs_lift theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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lift_lc [label="lift_lc", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="lift_lc theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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lift_0_lc [label="lift_0_lc", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="lift_0_lc theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_bvar [label="open_rec_bvar", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_bvar theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_fvar [label="close_rec_fvar", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_fvar theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_occurs_false [label="open_rec_occurs_false", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_occurs_false theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_notin [label="close_rec_notin", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_notin theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_fvs [label="close_rec_fvs", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_fvs theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_bvar_neq [label="open_rec_bvar_neq", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_bvar_neq theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_fvs [label="open_rec_fvs", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_fvs theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_close [label="open_close", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_close theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_fvar_self [label="subst_fvar_self", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_fvar_self theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_fvar_other [label="subst_fvar_other", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_fvar_other theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_fvs [label="subst_fvs", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_fvs theory/Binding.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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Plus_red1_context [label="Plus_red1_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Plus_red1_context theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_count_zero [label="occurs_count_zero", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_count_zero theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_count_false [label="occurs_count_false", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_count_false theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_count_pos [label="occurs_count_pos", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_count_pos theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_lift_self [label="occurs_lift_self", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_lift_self theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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zdecs_nonempty [label="zdecs_nonempty", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="zdecs_nonempty theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_count_zfill_plug [label="occurs_count_zfill_plug", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_count_zfill_plug theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_zplug_lift [label="open_rec_zplug_lift", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_zplug_lift theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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full_comp_aux [label="full_comp_aux", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="full_comp_aux theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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lemma_2_2_full_comp [label="lemma_2_2_full_comp", color="#38761d", fillcolor="#d9ead3", style="rounded,filled", fontcolor="#222222", tooltip="lemma_2_2_full_comp (section 2.2) theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=box];
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fvs_zplug_lift [label="fvs_zplug_lift", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="fvs_zplug_lift theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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plug_fv_mono [label="plug_fv_mono", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="plug_fv_mono theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red1_root_fv [label="red1_root_fv", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red1_root_fv theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red1r_fv [label="red1r_fv", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red1r_fv theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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lemma_2_1_fv_preserved [label="lemma_2_1_fv_preserved", color="#38761d", fillcolor="#d9ead3", style="rounded,filled", fontcolor="#222222", tooltip="lemma_2_1_fv_preserved (section 2.1) theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=box];
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lemma_2_3_beta_sim [label="lemma_2_3_beta_sim", color="#38761d", fillcolor="#d9ead3", style="rounded,filled", fontcolor="#222222", tooltip="lemma_2_3_beta_sim (section 2.3) theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=box];
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par_red1_iff [label="par_red1_iff", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="par_red1_iff theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red1_in_par [label="red1_in_par", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red1_in_par theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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par_context [label="par_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="par_context theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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par_to_red1_or_eq [label="par_to_red1_or_eq", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="par_to_red1_or_eq theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red1_or_eq_to_par [label="red1_or_eq_to_par", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red1_or_eq_to_par theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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par_reflexive [label="par_reflexive", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="par_reflexive theory/Parallel.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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gen_list_length [label="gen_list_length", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="gen_list_length theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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check_term_true [label="check_term_true", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="check_term_true theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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check_all_true [label="check_all_true", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="check_all_true theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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gen_sound [label="gen_sound", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="gen_sound theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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gen_complete [label="gen_complete", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="gen_complete theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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gen_fv_preserved [label="gen_fv_preserved", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="gen_fv_preserved theory/Random.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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zdecs_sound [label="zdecs_sound", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="zdecs_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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zdecs_complete [label="zdecs_complete", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="zdecs_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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positions_at [label="positions_at", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="positions_at theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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root_steps_sound [label="root_steps_sound", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="root_steps_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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root_steps_complete [label="root_steps_complete", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="root_steps_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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steps_sound [label="steps_sound", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="steps_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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steps_sound_red1 [label="steps_sound_red1", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="steps_sound_red1 theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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positions_hole [label="positions_hole", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="positions_hole theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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root_steps_in_steps [label="root_steps_in_steps", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="root_steps_in_steps theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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plug_comp [label="plug_comp", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="plug_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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positions_comp [label="positions_comp", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="positions_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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at_ctx_comp [label="at_ctx_comp", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="at_ctx_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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steps_complete [label="steps_complete", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="steps_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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has_red_f [label="has_red_f", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="has_red_f theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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has_red_spec [label="has_red_spec", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="has_red_spec theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red1_dec [label="red1_dec", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red1_dec theory/Reduction.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_app [label="open_rec_app", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_app theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_lam [label="open_rec_lam", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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open_rec_esub [label="open_rec_esub", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="open_rec_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_app [label="close_rec_app", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_app theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_lam [label="close_rec_lam", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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close_rec_esub [label="close_rec_esub", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="close_rec_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_app [label="subst_app", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_app theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_lam [label="subst_lam", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_esub [label="subst_esub", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_notin [label="subst_notin", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_notin theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_lc_self [label="subst_lc_self", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_lc_self theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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subst_other [label="subst_other", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="subst_other theory/Substitution.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red_sub_root_to_red1 [label="red_sub_root_to_red1", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_sub_root_to_red1 theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red_sub_to_red1 [label="red_sub_to_red1", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_sub_to_red1 theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red_sub_context [label="red_sub_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_sub_context theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red_sub_gc [label="red_sub_gc", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_sub_gc theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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red_sub_r [label="red_sub_r", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="red_sub_r theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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occurs_zfill [label="occurs_zfill", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="occurs_zfill theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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zfill_occurs0 [label="zfill_occurs0", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="zfill_occurs0 theory/Subsystem.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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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];
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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];
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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];
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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];
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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];
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lift_lc -> lift_0_lc;
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fvs_lift -> open_rec_fvs;
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open_rec_bvar -> open_rec_fvs;
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open_rec_bvar_neq -> open_rec_fvs;
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open_rec_bvar -> open_close;
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lift_0_lc -> subst_fvar_self;
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close_rec_fvs -> subst_fvs;
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open_rec_fvs -> subst_fvs;
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occurs_count_zero -> occurs_count_pos;
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occurs_count_false -> occurs_count_zfill_plug;
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occurs_lift_self -> occurs_count_zfill_plug;
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occurs_lift_self -> open_rec_zplug_lift;
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open_rec_occurs_false -> open_rec_zplug_lift;
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occurs_count_zero -> full_comp_aux;
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occurs_count_zfill_plug -> full_comp_aux;
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open_rec_occurs_false -> full_comp_aux;
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open_rec_zplug_lift -> full_comp_aux;
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zdecs_nonempty -> full_comp_aux;
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zdecs_sound -> full_comp_aux;
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full_comp_aux -> lemma_2_2_full_comp;
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fvs_lift -> fvs_zplug_lift;
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fvs_zplug_lift -> red1_root_fv;
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plug_fv_mono -> red1r_fv;
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red1_root_fv -> red1r_fv;
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red1r_fv -> lemma_2_1_fv_preserved;
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Plus_red1_context -> lemma_2_3_beta_sim;
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lemma_2_2_full_comp -> lemma_2_3_beta_sim;
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par_red1_iff -> par_to_red1_or_eq;
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par_red1_iff -> red1_or_eq_to_par;
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has_red_spec -> check_term_true;
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steps_sound_red1 -> check_term_true;
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check_term_true -> check_all_true;
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steps_sound -> gen_sound;
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steps_complete -> gen_complete;
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lemma_2_1_fv_preserved -> gen_fv_preserved;
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steps_sound_red1 -> gen_fv_preserved;
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zdecs_sound -> root_steps_sound;
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zdecs_complete -> root_steps_complete;
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positions_at -> steps_sound;
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root_steps_sound -> steps_sound;
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steps_sound -> steps_sound_red1;
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positions_hole -> root_steps_in_steps;
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at_ctx_comp -> steps_complete;
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plug_comp -> steps_complete;
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positions_comp -> steps_complete;
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root_steps_complete -> steps_complete;
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root_steps_in_steps -> steps_complete;
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has_red_f -> has_red_spec;
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steps_complete -> has_red_spec;
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steps_sound -> has_red_spec;
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has_red_spec -> red1_dec;
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close_rec_notin -> subst_notin;
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open_rec_occurs_false -> subst_notin;
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subst_fvar_self -> subst_lc_self;
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subst_fvar_other -> subst_other;
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red_sub_root_to_red1 -> red_sub_to_red1;
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occurs_zfill -> zfill_occurs0;
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zfill_occurs0 -> R_Gc_disjoint;
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steps_sound -> corpus_sound;
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steps_complete -> corpus_complete;
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has_red_spec -> corpus_decides;
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lemma_2_1_fv_preserved -> corpus_fv_preserved;
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steps_sound_red1 -> corpus_fv_preserved;
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}
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