matita/matita/contribs/lambdadelta/apps_2/etc/models/model_nlift.etc

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   3 (*      ||M||                                                             *)
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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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  13 (**************************************************************************)
  14
  15 include "basic_2/substitution/lift_neg.ma".
  16 include "apps_2/models/model_sound.ma".
  17
  18 (* MODEL ********************************************************************)
  19
  20 lemma sound_ti_eq_nlift: ∀M. sound M → ∀sv,gv,U,lv1,lv2.
  21                          (∀i. (∀T. ⬆[i, 1]T ≡ U → ⊥) → lv1 i = lv2 i) →
  22                          〚U〛⦋M⦌{sv, gv, lv1} = 〚U〛⦋M⦌{sv, gv, lv2}.
  23 #M #HM #sv #gv #U elim U -U * [||| #a * | * ]
  24 [ #k #lv1 #lv2 #H >(m1 … HM) >(m1 … HM) -HM //
  25 | #i #lv1 #lv2 #H >(m2 … HM) >(m2 … HM) -HM
  26   /3 width=7 by lift_inv_lref2_be/
  27 | #p #lv1 #lv2 #H >(m3 … HM) >(m3 … HM) -HM //
  28 | #W #U #IHW #IHU #lv1 #lv2 #H >(m4 … HM) >(m4 … HM)
  29   @IHU -IHU #i @(nat_ind_plus … i) -i
  30   [ /5 width=9 by nlift_bind_sn/
  31   | #i #_ #H0 >raise_gt // >raise_gt //
  32     /4 width=9 by nlift_bind_dx/
  33   ]
  34 | #W #U #IHW #IHU #lv1 #lv2 #H @(m5 … HM) /5 width=9 by nlift_bind_sn/
  35   #d @IHU -IHU #i @(nat_ind_plus … i) -i //
  36   #i #_ #H0 lapply (nlift_bind_dx … H0) -H0
  37   #H0 lapply (H i ?) -H /2 width=5 by/ -H0 #H
  38   >raise_gt // >raise_gt //
  39 | #W #U #IHW #IHU #lv1 #lv2 #H >(m6 … HM) >(m6 … HM)
  40   /6 width=8 by nlift_flat_sn, nlift_flat_dx, eq_f2/
  41 | #W #U #_ #IHU #lv1 #lv2 #H >(m7 … HM) >(m7 … HM)
  42   /5 width=8 by nlift_flat_dx/
  43 ]
  44 qed-.