matita/matita/contribs/lambdadelta/basic_2A/reduction/crr_lift.ma

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   5 (*      ||T||                                                             *)
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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_2A/substitution/drop_drop.ma".
  16 include "basic_2A/reduction/crr.ma".
  17
  18 (* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE REDUCTION **************************)
  19
  20 (* Properties on relocation *************************************************)
  21
  22 lemma crr_lift: ∀G,K,T. ⦃G, K⦄ ⊢ ➡ 𝐑⦃T⦄ → ∀L,s,l,m. ⬇[s, l, m] L ≡ K →
  23                 ∀U. ⬆[l, m] T ≡ U → ⦃G, L⦄ ⊢ ➡ 𝐑⦃U⦄.
  24 #G #K #T #H elim H -K -T
  25 [ #K #K0 #V #i #HK0 #L #s #l #m #HLK #X #H
  26   elim (lift_inv_lref1 … H) -H * #Hil #H destruct
  27   [ elim (drop_trans_lt … HLK … HK0) -K /2 width=4 by crr_delta/
  28   | lapply (drop_trans_ge … HLK … HK0 ?) -K /3 width=4 by crr_delta, drop_inv_gen/
  29   ]
  30 | #K #V #T #_ #IHV #L #s #l #m #HLK #X #H
  31   elim (lift_inv_flat1 … H) -H #W #U #HVW #_ #H destruct /3 width=5 by crr_appl_sn/
  32 | #K #V #T #_ #IHT #L #s #l #m #HLK #X #H
  33   elim (lift_inv_flat1 … H) -H #W #U #_ #HTU #H destruct /3 width=5 by crr_appl_dx/
  34 | #I #K #V #T #HI #L #s #l #m #_ #X #H
  35   elim (lift_fwd_pair1 … H) -H #W #U #_ #H destruct /2 width=1 by crr_ri2/
  36 | #a #I #K #V #T #HI #_ #IHV #L #s #l #m #HLK #X #H
  37   elim (lift_inv_bind1 … H) -H #W #U #HVW #_ #H destruct /3 width=5 by crr_ib2_sn/
  38 | #a #I #K #V #T #HI #_ #IHT #L #s #l #m #HLK #X #H
  39   elim (lift_inv_bind1 … H) -H #W #U #HVW #HTU #H destruct /4 width=5 by crr_ib2_dx, drop_skip/
  40 | #a #K #V #V0 #T #L #s #l #m #_ #X #H
  41   elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
  42   elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1 by crr_beta/
  43 | #a #K #V #V0 #T #L #s #l #m #_ #X #H
  44   elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
  45   elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1 by crr_theta/
  46 ]
  47 qed.
  48
  49 lemma crr_inv_lift: ∀G,L,U. ⦃G, L⦄ ⊢ ➡ 𝐑⦃U⦄ → ∀K,s,l,m. ⬇[s, l, m] L ≡ K →
  50                     ∀T. ⬆[l, m] T ≡ U → ⦃G, K⦄ ⊢ ➡ 𝐑⦃T⦄.
  51 #G #L #U #H elim H -L -U
  52 [ #L #L0 #W #i #HK0 #K #s #l #m #HLK #X #H
  53   elim (lift_inv_lref2 … H) -H * #Hil #H destruct
  54   [ elim (drop_conf_lt … HLK … HK0) -L /2 width=4 by crr_delta/
  55   | lapply (drop_conf_ge … HLK … HK0 ?) -L /2 width=4 by crr_delta/
  56   ]
  57 | #L #W #U #_ #IHW #K #s #l #m #HLK #X #H
  58   elim (lift_inv_flat2 … H) -H #V #T #HVW #_ #H destruct /3 width=5 by crr_appl_sn/
  59 | #L #W #U #_ #IHU #K #s #l #m #HLK #X #H
  60   elim (lift_inv_flat2 … H) -H #V #T #_ #HTU #H destruct /3 width=5 by crr_appl_dx/
  61 | #I #L #W #U #HI #K #s #l #m #_ #X #H
  62   elim (lift_fwd_pair2 … H) -H #V #T #_ #H destruct /2 width=1 by crr_ri2/
  63 | #a #I #L #W #U #HI #_ #IHW #K #s #l #m #HLK #X #H
  64   elim (lift_inv_bind2 … H) -H #V #T #HVW #_ #H destruct /3 width=5 by crr_ib2_sn/
  65 | #a #I #L #W #U #HI #_ #IHU #K #s #l #m #HLK #X #H
  66   elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct /4 width=5 by crr_ib2_dx, drop_skip/
  67 | #a #L #W #W0 #U #K #s #l #m #_ #X #H
  68   elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
  69   elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1 by crr_beta/
  70 | #a #L #W #W0 #U #K #s #l #m #_ #X #H
  71   elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
  72   elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1 by crr_theta/
  73 ]
  74 qed-.