matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl

   1 name "basic_2_src"
   2
   3 table {
   4    class "gray"
   5    [ { "component" * } {
   6         [ { "section" * } {
   7              [ [ "plane" ] "files" * ]
   8           }
   9         ]
  10      }
  11    ]
  12 (*
  13    class "wine"
  14    [ { "" * } {
  15         [ { "" * } {
  16              [ [ "" ] "" * ]
  17           }
  18         ]
  19      }
  20    ]
  21 (*
  22    [ { "higher order dynamic typing" * } {
  23         [ { "higher order native type assignment" * } {
  24              [ [ "" ] "ntas ( ⦃?,?⦄ ⊢ ? :* ? )" "nta_lift" * ]
  25           }
  26         ]
  27      }
  28    ]
  29 *)
  30    class "magenta"
  31    [ { "dynamic typing" * } {
  32 (*
  33         [ { "local env. ref. for native type assignment" * } {
  34              [ [ "" ] "lsubn ( ? ⊢ ? :⫃ ? )" "lsubn_drop" "lsubn_cpcs" "lsubn_nta" * ]
  35           }
  36         ]
  37         [ { "native type assignment" * } {
  38              [ [ "" ] "nta ( ⦃?,?⦄ ⊢ ? : ? )" "nta_alt ( ⦃?,?⦄ ⊢ ? :: ? )" "nta_lift" "nta_ltpss" "nta_thin" "nta_aaa" "nta_sta" "nta_ltpr" "nta_nta" * ]
  39           }
  40         ]
  41 *)
  42         [ { "local env. ref. for stratified native validity" * } {
  43              [ [ "" ] "lsubsv ( ? ⊢ ? ⫃¡[?,?] ? )" "lsubsv_lsuba" + "lsubsv_lsubd" + "lsubsv_lstas" + "lsubsv_scpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
  44           }
  45         ]
  46         [ { "stratified native validity" * } {
  47              [ [ "" ] "shnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] )" * ]
  48              [ [ "" ] "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_da_lpr" + "snv_lstas" + "snv_lstas_lpr" + "snv_lpr" + "snv_fsb" + "snv_scpes" + "snv_preserve" * ]
  49           }
  50         ]
  51      }
  52    ]
  53    class "prune"
  54    [ { "equivalence" * } {
  55         [ { "decomposed rt-equivalence" * } {
  56              [ [ "" ] "scpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? )" "scpes_aaa" + "scpes_cpcs" + "scpes_scpes" * ]
  57           }
  58         ]
  59         [ { "context-sensitive equivalence" * } {
  60              [ [ "" ] "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
  61           }
  62         ]
  63      }
  64    ]
  65 *)
  66    class "blue"
  67    [ { "rt-conversion" * } {
  68         [ { "context-sensitive parallel r-conversion" * } {
  69              [ [ "for terms" ] "cpc" + "( ⦃?,?⦄ ⊢ ? ⬌[?] ? )" "cpc_cpc" * ]
  70           }
  71         ]
  72      }
  73    ]
  74    class "sky"
  75    [ { "rt-computation" * } {
  76 (*
  77         [ { "evaluation for context-sensitive rt-reduction" * } {
  78              [ [ "" ] "cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )" * ]
  79           }
  80         ]
  81         [ { "evaluation for context-sensitive reduction" * } {
  82              [ [ "" ] "cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
  83           }
  84         ]
  85         [ { "strongly normalizing qrst-computation" * } {
  86              [ [ "" ] "fsb ( ⦥[?,?] ⦃?,?,?⦄ )" "fsb_alt ( ⦥⦥[?,?] ⦃?,?,?⦄ )" "fsb_aaa" + "fsb_csx" * ]
  87           }
  88         ]
  89         [ { "strongly normalizing rt-computation" * } {
  90              [ [ "" ] "llsx_csx" * ]
  91              [ [ "" ] "csx_fpbs" * ]
  92           }
  93         ]
  94         [ { "parallel qrst-computation" * } {
  95              [ [ "" ] "fpbg ( ⦃?,?,?⦄ >≛[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbs" + "fpbg_fpbg" * ]
  96              [ [ "" ] "fpbs_alt" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_fpbs" * ]
  97           }
  98         ]
  99         [ { "decomposed rt-computation" * } {
 100              [ [ "" ] "scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )" "scpds_lift" + "scpds_aaa" + "scpds_scpds" * ]
 101           }
 102         ]
 103         [ { "context-sensitive computation" * } {
 104              [ [ "" ] "lprs ( ⦃?,?⦄ ⊢ ➡* ? )" "lprs_drop" + "lprs_cprs" + "lprs_lprs" * ]
 105              [ [ "" ] "cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
 106           }
 107         ]
 108 *)
 109         [ { "uncounted context-sensitive parallel rst-computation" * } {
 110              [ [ "for closures" ] "fpbs" + "( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_fqup" + "fpbs_fqus" + "fpbs_cpxs" + "fpbs_lfpxs" * ]
 111           }
 112         ]
 113         [ { "uncounted context-sensitive parallel rt-computation" * } {
 114              [ [ "refinement for lenvs on selected entries" ] "lsubsx" + "( ? ⊢ ? ⊆ⓧ[?,?,?] ? )" "lsubsx_lfsx" + "lsubsx_lsubsx" * ]
 115              [ [ "strongly normalizing for lenvs on referred entries" ] "lfsx" + "( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )" "lfsx_drops" + "lfsx_fqup" + "lfsx_cpx" + "lfsx_cpxs" + "lfsx_lfpxs" + "lfsx_lfsx" * ]
 116              [ [ "strongly normalizing for term vectors" ] "csx_vector" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_cnx_vector" + "csx_csx_vector" * ]
 117              [ [ "strongly normalizing for terms" ] "csx" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_fqus" + "csx_lsubr" + "csx_lfdeq" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_cpxs" + "csx_lfpxs" + "csx_csx" * ]
 118              [ [ "for lenvs on referred entries" ] "lfpxs" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_ffdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lpxs" + "lfpxs_lfpxs" * ]
 119              [ [ "for lenvs on all entries" ] "lpxs" + "( ⦃?,?⦄ ⊢ ⬈*[?] ? )" "lpxs_length" + "lpxs_lpx" + "lpxs_cpxs" * ]
 120              [ [ "for binders" ] "cpxs_ext" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" * ]
 121              [ [ "for terms" ] "cpxs" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_lfdeq" + "cpxs_ffdeq" + "cpxs_aaa" + "cpxs_lpx" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ]
 122           }
 123         ]
 124      }
 125    ]
 126    class "cyan"
 127    [ { "rt-transition" * } {
 128         [ { "uncounted parallel rst-transition" * } {
 129              [ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" + "fpbq_fpb" * ]
 130              [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" + "fpb_ffdeq" * ]
 131           }
 132         ]
 133         [ { "context-sensitive parallel r-transition" * } {
 134              [ [ "for lenvs on referred entries" ] "lfpr" + "( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fquq" + "lfpr_fqup" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
 135              [ [ "for binders" ] "cpr_ext" + "( ⦃?,?⦄ ⊢ ? ➡[?] ? )" * ]
 136              [ [ "for terms" ] "cpr" + "( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" * ]
 137           }
 138         ]
 139         [ { "t-bound context-sensitive parallel rt-transition" * } {
 140              [ [ "for terms" ] "cpm" + "( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpm_simple" + "cpm_drops" + "cpm_lsubr" + "cpm_fsle" + "cpm_cpx" * ]
 141           }
 142         ]
 143         [ { "uncounted context-sensitive parallel rt-transition" * } {
 144              [ [ "normal form for terms" ] "cnx" + "( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" + "cnx_cnx" * ]
 145              [ [ "for lenvs on referred entries" ] "lfpx" + "( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fquq" + "lfpx_fqup" + "lfpx_fsle" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_lpx" + "lfpx_lfpx" * ]
 146              [ [ "for lenvs on all entries" ] "lpx" + "( ⦃?,?⦄ ⊢ ⬈[?] ? )" * ]
 147              [ [ "for binders" ] "cpx_ext" + "( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" * ]
 148              [ [ "for terms" ] "cpx" + "( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfeq" + "cpx_lfdeq" * ]
 149           }
 150         ]
 151         [ { "counted context-sensitive parallel rt-transition" * } {
 152              [ [ "for terms" ] "cpg" + "( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )" "cpg_simple" + "cpg_drops" + "cpg_lsubr" * ]
 153           }
 154         ]
 155      }
 156    ]
 157    class "water"
 158    [ { "iterated static typing" * } {
 159         [ { "iterated generic extension of a context-sensitive relation" * } {
 160              [ [ "for lenvs on referred entries" ] "tc_lfxs" + "( ? ⦻**[?,?] ? )" "tc_lfxs_length" + "tc_lfxs_lex" + "tc_lfxs_drops" + "tc_lfxs_fqup" + "tc_lfxs_tc_lfxs" * ]
 161           }
 162         ]
 163      }
 164    ]
 165    class "green"
 166    [ { "static typing" * } {
 167         [ { "generic reducibility" * } {
 168              [ [ "restricted refinement for lenvs" ] "lsubc" + "( ? ⊢ ? ⫃[?] ? )" "lsubc_drops" + "lsubc_lsubr" + "lsubc_lsuba" * ]
 169              [ [ "candidates" ] "gcp_cr" + "( ⦃?,?,?⦄ ϵ[?] 〚?〛 )" "gcp_aaa" * ]
 170              [ [ "computation properties" ] "gcp" *]
 171           }
 172         ]
 173         [ { "atomic arity assignment" * } {
 174              [ [ "restricted refinement for lenvs" ] "lsuba" + "( ? ⊢ ? ⫃⁝ ? )" "lsuba_drops" + "lsuba_lsubr" + "lsuba_aaa" + "lsuba_lsuba" * ]
 175              [ [ "for terms" ] "aaa" + "( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_drops" + "aaa_fqus" + "aaa_lfdeq" + "aaa_ffdeq" + "aaa_aaa" * ]
 176           }
 177         ]
 178         [ { "degree-based equivalence" * } {
 179              [ [ "for closures on referred entries" ] "ffdeq" + "( ⦃?,?,?⦄ ≛[?,?] ⦃?,?,?⦄ )" "ffdeq_fqup" + "ffdeq_fqus" + "ffdeq_ffdeq" * ]
 180              [ [ "for lenvs on referred entries" ] "lfdeq" + "( ? ≛[?,?,?] ? )" "lfdeq_length" + "lfdeq_drops" + "lfdeq_fqup" + "lfdeq_fqus" + "lfdeq_lfeq" + "lfdeq_lfdeq" * ]
 181           }
 182         ]
 183         [ { "syntactic equivalence" * } {
 184              [ [ "for lenvs on referred entries" ] "lfeq" + "( ? ≐[?] ? )" "lfeq_fqup" + "lfeq_fsle" * ]
 185           }
 186         ]
 187         [ { "generic extension of a context-sensitive relation" * } {
 188              [ [ "for lenvs on referred entries" ] "lfxs" + "( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_lex" + "lfxs_drops" + "lfxs_fqup" + "lfxs_fsle" + "lfxs_lfxs" * ]
 189           }
 190         ]
 191         [ { "context-sensitive free variables" * } {
 192              [ [ "inclusion for restricted closures" ] "fsle" + "( ⦃?,?⦄ ⊆ ⦃?,?⦄ )" "fsle_length" + "fsle_drops" + "fsle_fqup" + "fsle_fsle" * ]
 193              [ [ "restricted refinement for lenvs" ] "lsubf" + "( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )" "lsubf_lsubr" + "lsubf_frees" + "lsubf_lsubf" * ]
 194              [ [ "for terms" ] "frees" + "( ? ⊢ 𝐅*⦃?⦄ ≡ ? )" "frees_append" + "frees_drops" + "frees_fqup" + "frees_frees" * ]
 195           }
 196         ]
 197         [ { "local environments" * } {
 198              [ [ "restricted refinement" ] "lsubr" + "( ? ⫃ ? )" "lsubr_length" + "lsubr_drops" + "lsubr_lsubr" * ]
 199           }
 200         ]
 201      }
 202    ]
 203    class "grass"
 204    [ { "s-computation" * } {
 205         [ { "iterated structural successor" * } {
 206              [ [ "for closures" ] "fqus" + "( ⦃?,?,?⦄ ⊐*[?] ⦃?,?,?⦄ )" + "( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )" "fqus_weight" + "fqus_drops" + "fqus_fqup" + "fqus_fqus" * ]
 207              [ [ "proper for closures" ] "fqup" + "( ⦃?,?,?⦄ ⊐+[?] ⦃?,?,?⦄ )" + "( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )" "fqup_weight" + "fqup_drops" + "fqup_fqup" * ]
 208           }
 209         ]
 210      }
 211    ]
 212    class "yellow"
 213    [ { "s-transition" * } {
 214         [ { "structural successor" * } {
 215              [ [ "for closures" ] "fquq" + "( ⦃?,?,?⦄ ⊐⸮[?] ⦃?,?,?⦄ )" + "( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )" "fquq_length" + "fquq_weight" * ]
 216              [ [ "proper for closures" ] "fqu" + "( ⦃?,?,?⦄ ⊐[?] ⦃?,?,?⦄ )" + "( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )" "fqu_length" + "fqu_weight" + "fqu_tdeq" * ]
 217           }
 218         ]
 219      }
 220    ]
 221    class "orange"
 222    [ { "relocation" * } {
 223         [ { "generic slicing" * } {
 224              [ [ "for lenvs" ] "drops" + "( ⬇*[?,?] ? ≡ ? )" + "( ⬇*[?] ? ≡ ? )" "drops_lstar" + "drops_weight" + "drops_length" + "drops_cext2" + "drops_lexs" + "drops_lreq" + "drops_drops" + "drops_vector" * ]
 225           }
 226         ]
 227         [ { "generic relocation" * } {
 228              [ [ "for binders" ] "lifts_bind" + "( ⬆*[?] ? ≡ ? )" "lifts_weight_bind" + "lifts_lifts_bind" * ]
 229              [ [ "for term vectors" ] "lifts_vector" + "( ⬆*[?] ? ≡ ? )" "lifts_lifts_vector" * ]
 230              [ [ "for terms" ] "lifts" + "( ⬆*[?] ? ≡ ? )" "lifts_simple" + "lifts_weight" + "lifts_tdeq" + "lifts_lifts" * ]
 231           }
 232         ]
 233         [ { "syntactic equivalence" * } {
 234              [ [ "for lenvs on selected entries" ] "lreq" + "( ? ≐[?] ? )" "lreq_length" + "lreq_lreq" * ]
 235           }
 236         ]
 237         [ { "generic entrywise extension" * } {
 238              [ [ "for lenvs of one contex-sensitive relation" ] "lex" + "( ? ⦻[?] ? )" "lex_tc" + "lex_length" * ]
 239              [ [ "for lenvs of two contex-sensitive relations" ] "lexs" + "( ? ⦻*[?,?,?] ? )" "lexs_tc" + "lexs_length" + "lexs_lexs" * ]
 240           }
 241         ]
 242      }
 243    ]
 244    class "red"
 245    [ { "syntax" * } {
 246         [ { "equivalence up to exclusion binders" * } {
 247              [ [ "for lenvs" ] "lveq" + "( ? ≋ⓧ*[?,?] ? )" "lveq_length" + "lveq_lveq" * ]
 248           }
 249         ]
 250         [ { "append" * } {
 251              [ [ "for lenvs" ] "append" + "( ? @@ ? )" "append_length" * ]
 252           }
 253         ]
 254         [ { "head equivalence" * } {
 255              [ [ "for terms" ] "theq" + "( ? ⩳[?,?] ? )" "theq_simple" + "theq_tdeq" + "theq_theq" + "theq_simple_vector" * ]
 256           }
 257         ]
 258         [ { "degree-based equivalence" * } {
 259              [ [ "" ] "tdeq_ext" + "( ? ≛[?,?] ? )" + "( ? ⊢ ? ≛[?,?] ? )" * ]
 260              [ [ "" ] "tdeq" + "( ? ≛[?,?] ? )" "tdeq_tdeq" * ]
 261           }
 262         ]
 263         [ { "closures" * } {
 264              [ [ "" ] "cl_weight" + "( ♯{?,?,?} )" * ]
 265              [ [ "" ] "cl_restricted_weight" + "( ♯{?,?} )" * ]
 266           }
 267         ]
 268         [ { "global environments" * } {
 269              [ [ "" ] "genv" * ]
 270           }
 271         ]
 272         [ { "local environments" * } {
 273              [ [ "" ] "ceq_ext" "ceq_ext_ceq_ext" * ]
 274              [ [ "" ] "cext2" * ]
 275              [ [ "" ] "lenv_length" + "( |?| )" * ]
 276              [ [ "" ] "lenv_weight" + "( ♯{?} )" * ]
 277              [ [ "" ] "lenv" * ]
 278           }
 279         ]
 280         [ { "binders for local environments" * } {
 281              [ [ "" ] "ext2" "ext2_tc" + "ext2_ext2" * ]
 282              [ [ "" ] "bind" "bind_weight" * ]
 283           }
 284         ]
 285         [ { "terms" * } {
 286              [ [ "" ] "term_vector" + "( Ⓐ?.? )" * ]
 287              [ [ "" ] "term_simple" + "( 𝐒⦃?⦄ )"  * ]
 288              [ [ "" ] "term_weight" + "( ♯{?} )" * ]
 289              [ [ "" ] "term" * ]
 290           }
 291         ]
 292         [ { "items" * } {
 293              [ [ "" ] "item_sd" * ]
 294              [ [ "" ] "item_sh" * ]
 295              [ [ "" ] "item" * ]
 296           }
 297         ]
 298         [ { "atomic arities" * } {
 299              [ [ "" ] "aarity" * ]
 300           }
 301         ]
 302      }
 303    ]
 304 }
 305
 306 class "top"               { * }
 307
 308 class "capitalize italic" { 0 1 }
 309
 310 class "italic"            { 2 }
 311 (*
 312         [ { "normal forms for context-sensitive rt-reduction" * } {
 313              [ [ "" ] "cnx_crx" + "cnx_cix" * ]
 314           }
 315         ]
 316         [ { "irreducible forms for context-sensitive rt-reduction" * } {
 317              [ [ "" ] "cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )" "cix_lift" * ]
 318           }
 319         ]
 320         [ { "reducible forms for context-sensitive rt-reduction" * } {
 321              [ [ "" ] "crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )" "crx_lift" * ]
 322           }
 323         ]
 324         [ { "normal forms for context-sensitive reduction" * } {
 325              [ [ "" ] "cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )" "cnr_lift" + "cnr_crr" + "cnr_cir" * ]
 326           }
 327         ]
 328         [ { "irreducible forms for context-sensitive reduction" * } {
 329              [ [ "" ] "cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )" "cir_lift" * ]
 330           }
 331         ]
 332         [ { "reducible forms for context-sensitive reduction" * } {
 333              [ [ "" ] "crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )" "crr_lift" * ]
 334           }
 335         ]
 336         [ { "unfold" * } {
 337              [ [ "" ] "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
 338           }
 339         ]
 340         [ { "iterated static type assignment" * } {
 341              [ [ "" ] "lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )" "lstas_lift" + "lstas_llpx_sn.ma" + "lstas_aaa" + "lstas_da" + "lstas_lstas" * ]
 342           }
 343         ]
 344         [ { "local env. ref. for degree assignment" * } {
 345              [ [ "" ] "lsubd ( ? ⊢ ? ⫃▪[?,?] ? )" "lsubd_da" + "lsubd_lsubd" * ]
 346           }
 347         ]
 348         [ { "degree assignment" * } {
 349              [ [ "" ] "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_aaa" + "da_da" * ]
 350           }
 351         ]
 352         [ { "context-sensitive multiple rt-substitution" * } {
 353              [ [ "" ] "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
 354           }
 355         ]
 356         [ { "pointwise union for local environments" * } {
 357              [ [ "" ] "llor ( ? ⋓[?,?] ? ≡ ? )" "llor_alt" + "llor_drop" * ]
 358           }
 359         ]
 360         [ { "lazy pointwise extension of a relation" * } {
 361              [ [ "" ] "llpx_sn" "llpx_sn_alt" + "llpx_sn_alt_rec" + "llpx_sn_tc" + "llpx_sn_lreq" + "llpx_sn_drop" + "llpx_sn_lpx_sn" + "llpx_sn_frees" + "llpx_sn_llor" * ]
 362           }
 363         ]
 364         [ { "global env. slicing" * } {
 365              [ [ "" ] "gget ( ⬇[?] ? ≡ ? )" "gget_gget" * ]
 366           }
 367         ]
 368         [ { "context-sensitive ordinary rt-substitution" * } {
 369              [ [ "" ] "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
 370           }
 371         ]
 372         [ { "local env. ref. for rt-substitution" * } {
 373              [ [ "" ] "lsuby ( ? ⊆[?,?] ? )" "lsuby_lsuby" * ]
 374           }
 375         ]
 376         [ { "pointwise extension of a relation" * } {
 377              [ [ "" ] "lpx_sn" "lpx_sn_alt" + "lpx_sn_drop" + "lpx_sn_lpx_sn" * ]
 378           }
 379         ]
 380              [ [ "" ] "cpx_lreq" + "cpr_cir" + "fpb_lift" + "fpbq_lift" ]
 381              [ [ "" ] "lleq ( ? ≡[?,?] ? )" "lleq_alt" + "lleq_alt_rec" + "lleq_lreq" + "lleq_drop" + "lleq_fqus" + "lleq_llor" + "lleq_lleq" * ]
 382 *)