matita/matita/contribs/lambda_delta/basic_2/etc/sta/sta_sta.etc

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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/ldrop_ldrop.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,L,T,U1. ⦃h, L⦄ ⊢ T • U1 →
  24                   ∀U2. ⦃h, L⦄ ⊢ T • U2 → U1 = U2.
  25 #h #L #T #U1 #H elim H -L -T -U1
  26 [ #L #k #X #H >(sta_inv_sort1 … H) -X //
  27 | #L #K #V #W #U1 #i #HLK #_ #HWU1 #IHVW #U2 #H
  28   elim (sta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
  29   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  30   lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
  31   >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
  32 | #L #K #W #V #U1 #i #HLK #_ #HWU1 #IHWV #U2 #H
  33   elim (sta_inv_lref1 … H) -H * #K0 #W0 #V0 #HLK0 #HWV0 #HV0U2
  34   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  35   lapply (IHWV … HWV0) -IHWV -HWV0 #H destruct
  36   >(lift_mono … HWU1 … HV0U2) -W -U1 //
  37 | #I #L #V #T #U1 #_ #IHTU1 #X #H
  38   elim (sta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
  39 | #L #V #T #U1 #_ #IHTU1 #X #H
  40   elim (sta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
  41 | #L #W #T #U1 #_ #IHTU1 #U2 #H
  42   lapply (sta_inv_cast1 … H) -H /2 width=1/
  43 ]
  44 qed-.