matita/matita/contribs/lambdadelta/basic_2/static/ssta_ssta.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/static/da_da.ma".
  16 include "basic_2/static/ssta_lift.ma".
  17
  18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 lemma ssta_inv_refl_pos: ∀h,g,G,L,T,l.  ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] T → ⊥.
  23 #h #g #G #L #T #l #H1T #HTT
  24 lapply (ssta_da_conf … HTT … H1T) -HTT <minus_plus_m_m #H2T
  25 lapply (da_mono … H2T … H1T) -h -G -L -T #H
  26 elim (plus_xySz_x_false 0 l 0) //
  27 qed-.
  28
  29 (* Main properties **********************************************************)
  30
  31 theorem ssta_mono: ∀h,g,G,L. singlevalued … (ssta h g G L).
  32 #h #g #G #L #T #U1 #H elim H -G -L -T -U1
  33 [ #G #L #k #X #H >(ssta_inv_sort1 … H) -X //
  34 | #G #L #K #V #U1 #W #i #HLK #_ #HWU1 #IHVW #U2 #H
  35   elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
  36   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  37   lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
  38   >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
  39 | #G #L #K #W #U1 #l #i #HLK #HWl #HWU1 #U2 #H
  40   elim (ssta_inv_lref1 … H) -H * #K0 #W0 #l0 #HLK0 #HWl0 #HW0U2
  41   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
  42   lapply (da_mono … HWl0 … HWl) -HWl0 #H destruct
  43   >(lift_mono … HWU1 … HW0U2) -W -U1 //
  44 | #a #I #G #L #V #T #U1 #_ #IHTU1 #X #H
  45   elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
  46 | #G #L #V #T #U1 #_ #IHTU1 #X #H
  47   elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
  48 | #G #L #W #T #U1 #_ #IHTU1 #U2 #H
  49   lapply (ssta_inv_cast1 … H) -H /2 width=1/
  50 ]
  51 qed-.