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lambda-sub/graphs/theorems.json
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{
"paper": {
"title": "Milner's Lambda-Calculus with Partial Substitutions",
"authors": [
"Delia Kesner",
"Shane Ó Conchúir"
],
"url": "https://arxiv.org/abs/2312.13270",
"html": "https://arxiv.org/html/2312.13270v1"
},
"milestones": [
"M1",
"M2"
],
"current": "M2",
"nodes": [
{
"id": "fvs_lift",
"label": "fvs_lift",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "lift_lc",
"label": "lift_lc",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "lift_0_lc",
"label": "lift_0_lc",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": [
"lift_lc"
]
},
{
"id": "open_rec_bvar",
"label": "open_rec_bvar",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "close_rec_fvar",
"label": "close_rec_fvar",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "open_rec_occurs_false",
"label": "open_rec_occurs_false",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "close_rec_notin",
"label": "close_rec_notin",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "close_rec_fvs",
"label": "close_rec_fvs",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "open_rec_bvar_neq",
"label": "open_rec_bvar_neq",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "open_rec_fvs",
"label": "open_rec_fvs",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": [
"fvs_lift",
"open_rec_bvar",
"open_rec_bvar_neq"
]
},
{
"id": "open_close",
"label": "open_close",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": [
"open_rec_bvar"
]
},
{
"id": "subst_fvar_self",
"label": "subst_fvar_self",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": [
"lift_0_lc"
]
},
{
"id": "subst_fvar_other",
"label": "subst_fvar_other",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": []
},
{
"id": "subst_fvs",
"label": "subst_fvs",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Binding.v",
"depends": [
"close_rec_fvs",
"open_rec_fvs"
]
},
{
"id": "Plus_red1_context",
"label": "Plus_red1_context",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "occurs_count_zero",
"label": "occurs_count_zero",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "occurs_count_false",
"label": "occurs_count_false",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "occurs_count_pos",
"label": "occurs_count_pos",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"occurs_count_zero"
]
},
{
"id": "occurs_lift_self",
"label": "occurs_lift_self",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "zdecs_nonempty",
"label": "zdecs_nonempty",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "occurs_count_zfill_plug",
"label": "occurs_count_zfill_plug",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"occurs_count_false",
"occurs_lift_self"
]
},
{
"id": "open_rec_zplug_lift",
"label": "open_rec_zplug_lift",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"occurs_lift_self",
"open_rec_occurs_false"
]
},
{
"id": "full_comp_aux",
"label": "full_comp_aux",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"occurs_count_zero",
"occurs_count_zfill_plug",
"open_rec_occurs_false",
"open_rec_zplug_lift",
"zdecs_nonempty",
"zdecs_sound"
]
},
{
"id": "lemma_2_2_full_comp",
"label": "lemma_2_2_full_comp",
"kind": "paper",
"status": "proved",
"milestone": "M2",
"section": "2.2",
"file": "theory/Metatheory.v",
"depends": [
"full_comp_aux"
]
},
{
"id": "fvs_zplug_lift",
"label": "fvs_zplug_lift",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"fvs_lift"
]
},
{
"id": "plug_fv_mono",
"label": "plug_fv_mono",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": []
},
{
"id": "red1_root_fv",
"label": "red1_root_fv",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"fvs_zplug_lift"
]
},
{
"id": "red1r_fv",
"label": "red1r_fv",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Metatheory.v",
"depends": [
"plug_fv_mono",
"red1_root_fv"
]
},
{
"id": "lemma_2_1_fv_preserved",
"label": "lemma_2_1_fv_preserved",
"kind": "paper",
"status": "proved",
"milestone": "M2",
"section": "2.1",
"file": "theory/Metatheory.v",
"depends": [
"red1r_fv"
]
},
{
"id": "lemma_2_3_beta_sim",
"label": "lemma_2_3_beta_sim",
"kind": "paper",
"status": "proved",
"milestone": "M2",
"section": "2.3",
"file": "theory/Metatheory.v",
"depends": [
"Plus_red1_context",
"lemma_2_2_full_comp"
]
},
{
"id": "zdecs_sound",
"label": "zdecs_sound",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "zdecs_complete",
"label": "zdecs_complete",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "positions_at",
"label": "positions_at",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "root_steps_sound",
"label": "root_steps_sound",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"zdecs_sound"
]
},
{
"id": "root_steps_complete",
"label": "root_steps_complete",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"zdecs_complete"
]
},
{
"id": "steps_sound",
"label": "steps_sound",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"positions_at",
"root_steps_sound"
]
},
{
"id": "steps_sound_red1",
"label": "steps_sound_red1",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"steps_sound"
]
},
{
"id": "positions_hole",
"label": "positions_hole",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "root_steps_in_steps",
"label": "root_steps_in_steps",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"positions_hole"
]
},
{
"id": "plug_comp",
"label": "plug_comp",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "positions_comp",
"label": "positions_comp",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "at_ctx_comp",
"label": "at_ctx_comp",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "steps_complete",
"label": "steps_complete",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"at_ctx_comp",
"plug_comp",
"positions_comp",
"root_steps_complete",
"root_steps_in_steps"
]
},
{
"id": "has_red_f",
"label": "has_red_f",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": []
},
{
"id": "has_red_spec",
"label": "has_red_spec",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"has_red_f",
"steps_complete",
"steps_sound"
]
},
{
"id": "red1_dec",
"label": "red1_dec",
"kind": "infra",
"status": "proved",
"milestone": "M1",
"section": "",
"file": "theory/Reduction.v",
"depends": [
"has_red_spec"
]
},
{
"id": "corpus_sound",
"label": "corpus_sound",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Tests.v",
"depends": [
"steps_sound"
]
},
{
"id": "corpus_complete",
"label": "corpus_complete",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Tests.v",
"depends": [
"steps_complete"
]
},
{
"id": "corpus_decides",
"label": "corpus_decides",
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"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Tests.v",
"depends": [
"has_red_spec"
]
},
{
"id": "corpus_fv_preserved",
"label": "corpus_fv_preserved",
"kind": "infra",
"status": "proved",
"milestone": "M2",
"section": "",
"file": "theory/Tests.v",
"depends": [
"lemma_2_1_fv_preserved",
"steps_sound_red1"
]
}
]
}