matita/matita/contribs/lambdadelta/basic_2A/etc/sta/sta_sta.etc

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/substitution/drop_drop.ma".
  16 include "basic_2/static/sta.ma".
  17
  18 (* STATIC TYPE ASSIGNMENT ON TERMS ******************************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 (* Note: apparently this was missing in basic_1 *)
  23 theorem sta_mono: ∀h,G,L. singlevalued … (sta h G L).
  24 #h #G #L #T #U1 #H elim H -G -L -T -U1
  25 [ #G #L #k #X #H >(sta_inv_sort1 … H) -X //
  26 | #G #L #K #V #W #U1 #i #HLK #_ #HWU1 #IHVW #U2 #H
  27   elim (sta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
  28   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  29   lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
  30   >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
  31 | #G #L #K #W #V #U1 #i #HLK #_ #HWU1 #IHWV #U2 #H
  32   elim (sta_inv_lref1 … H) -H * #K0 #W0 #V0 #HLK0 #HWV0 #HV0U2
  33   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  34   lapply (IHWV … HWV0) -IHWV -HWV0 #H destruct
  35   >(lift_mono … HWU1 … HV0U2) -W -U1 //
  36 | #a #I #G #L #V #T #U1 #_ #IHTU1 #X #H
  37   elim (sta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1 by eq_f/
  38 | #G #L #V #T #U1 #_ #IHTU1 #X #H
  39   elim (sta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1 by eq_f/
  40 | #G #L #W #T #U1 #_ #IHTU1 #U2 #H
  41   lapply (sta_inv_cast1 … H) -H /2 width=1 by/
  42 ]
  43 qed-.