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add(named): a named metaterm calculus with the C equation and the RX rule (M5 named rules)

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sneeker committed 2026-09-22 22:15:00 +02:00
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graphs/dependency.dot
+17
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@@ -40,6 +40,15 @@ digraph theorem_deps {
mfvs_lift_m [label="mfvs_lift_m", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mfvs_lift_m theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mfvs_close_m [label="mfvs_close_m", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mfvs_close_m theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mfvs_open_m [label="mfvs_open_m", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mfvs_open_m theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
of_trm_plug [label="of_trm_plug", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="of_trm_plug theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_of_red1 [label="mred_of_red1", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_of_red1 theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_context [label="mred_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_context theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_term_context [label="mred_term_context", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_term_context theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
of_trm_moccurs [label="of_trm_moccurs", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="of_trm_moccurs theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
of_trm_moccurs0 [label="of_trm_moccurs0", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="of_trm_moccurs0 theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_B_intro [label="mred_B_intro", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_B_intro theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_gc_intro [label="mred_gc_intro", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_gc_intro theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
mred_r_intro [label="mred_r_intro", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="mred_r_intro theory/Metaterm.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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];
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];
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];
@@ -58,6 +67,12 @@ digraph theorem_deps {
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];
Plus_trans [label="Plus_trans", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Plus_trans theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
Plus_step_trans [label="Plus_step_trans", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Plus_step_trans theory/Metatheory.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
isubst_meta_in [label="isubst_meta_in", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="isubst_meta_in theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
isubst_meta_notin [label="isubst_meta_notin", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="isubst_meta_notin theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
eqC_in_Es [label="eqC_in_Es", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="eqC_in_Es theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
Es_refl_any [label="Es_refl_any", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Es_refl_any theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
Es_sym_any [label="Es_sym_any", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Es_sym_any theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
Es_trans_any [label="Es_trans_any", color="#38761d", fillcolor="#d9ead3", style="filled", fontcolor="#222222", tooltip="Es_trans_any theory/NamedMeta.v https://arxiv.org/html/2312.13270v1", shape=ellipse];
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];
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];
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];
@@ -138,6 +153,8 @@ digraph theorem_deps {
steps_complete -> enumerate_complete;
of_trm_lift -> of_trm_open;
mfvs_lift_m -> mfvs_open_m;
of_trm_plug -> mred_term_context;
of_trm_moccurs -> of_trm_moccurs0;
occurs_count_zero -> occurs_count_pos;
occurs_count_false -> occurs_count_zfill_plug;
occurs_lift_self -> occurs_count_zfill_plug;
graphs/dependency.png
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graphs/dependency.svg
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graphs/index.txt
+23
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@@ -1,4 +1,27 @@
status milestone kind name file
proved M0 infra Es_refl_any theory/NamedMeta.v
proved M0 infra Es_sym_any theory/NamedMeta.v
proved M0 infra Es_trans_any theory/NamedMeta.v
proved M0 infra eqC_in_Es theory/NamedMeta.v
proved M0 infra isubst_meta_in theory/NamedMeta.v
proved M0 infra isubst_meta_notin theory/NamedMeta.v
proved M0 infra mfvs_close_m theory/Metaterm.v
proved M0 infra mfvs_lift_m theory/Metaterm.v
proved M0 infra mfvs_open_m theory/Metaterm.v
proved M0 infra mred_B_intro theory/Metaterm.v
proved M0 infra mred_context theory/Metaterm.v
proved M0 infra mred_gc_intro theory/Metaterm.v
proved M0 infra mred_of_red1 theory/Metaterm.v
proved M0 infra mred_r_intro theory/Metaterm.v
proved M0 infra mred_term_context theory/Metaterm.v
proved M0 infra of_trm_close theory/Metaterm.v
proved M0 infra of_trm_fvs theory/Metaterm.v
proved M0 infra of_trm_injective theory/Metaterm.v
proved M0 infra of_trm_lift theory/Metaterm.v
proved M0 infra of_trm_moccurs theory/Metaterm.v
proved M0 infra of_trm_moccurs0 theory/Metaterm.v
proved M0 infra of_trm_open theory/Metaterm.v
proved M0 infra of_trm_plug theory/Metaterm.v
proved M1 infra at_ctx_comp theory/Reduction.v
proved M1 infra close_rec_fvar theory/Binding.v
proved M1 infra close_rec_fvs theory/Binding.v
graphs/theorems.json
+154
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@@ -373,6 +373,100 @@
"mfvs_lift_m"
]
},
{
"id": "of_trm_plug",
"label": "of_trm_plug",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "mred_of_red1",
"label": "mred_of_red1",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "mred_context",
"label": "mred_context",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "mred_term_context",
"label": "mred_term_context",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": [
"of_trm_plug"
]
},
{
"id": "of_trm_moccurs",
"label": "of_trm_moccurs",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "of_trm_moccurs0",
"label": "of_trm_moccurs0",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": [
"of_trm_moccurs"
]
},
{
"id": "mred_B_intro",
"label": "mred_B_intro",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "mred_gc_intro",
"label": "mred_gc_intro",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "mred_r_intro",
"label": "mred_r_intro",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/Metaterm.v",
"depends": []
},
{
"id": "Plus_red1_context",
"label": "Plus_red1_context",
@@ -582,6 +676,66 @@
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "isubst_meta_in",
"label": "isubst_meta_in",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "isubst_meta_notin",
"label": "isubst_meta_notin",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "eqC_in_Es",
"label": "eqC_in_Es",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "Es_refl_any",
"label": "Es_refl_any",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "Es_sym_any",
"label": "Es_sym_any",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "Es_trans_any",
"label": "Es_trans_any",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/NamedMeta.v",
"depends": []
},
{
"id": "par_red1_iff",
"label": "par_red1_iff",