matita/matita/contribs/lambdadelta/basic_2A/etc/tshf/cpr_tshf.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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  14
  15 include "basic_2/grammar/tshf.ma".
  16 include "basic_2/reduction/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
  19
  20 (* Forward lemmas on same head forms for terms ******************************)
  21
  22 lemma cpr_fwd_tshf1: ∀L,T1,T2. L ⊢ T1 ➡ T2 → T1 ≈ T1 →
  23                      T2 ≈ T1 ∨ (L = ⋆ → ⊥).
  24 #L #T1 #T2 #H elim H -L -T1 -T2
  25 [ /2 width=1/
  26 | #L #K #V1 #V2 #W2 #i #HLK #_ #_ #_ #_
  27   @or_intror #H destruct
  28   lapply (ldrop_inv_atom1 … HLK) -HLK #H destruct
  29 | #a #I #L #V1 #V2 #T1 #T2 #_ #_ #_ #_ #H
  30   elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct /2 width=1/
  31 | #I #L #V1 #V2 #T1 #T2 #_ #_ #_ #IHT12 #H
  32   elim (tshf_inv_flat1 … H) -H #W2 #U2 #HT1U2 #HT1 #_ #H1 #H2 destruct
  33   lapply (IHT12 HT1U2) -IHT12 -HT1U2 * #HUT2 /3 width=1/
  34   lapply (simple_tshf_repl_sn … HUT2 HT1) /3 width=1/
  35 | #L #V #T #T1 #T2 #_ #_ #_ #H
  36   elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct
  37 | #L #V #T1 #T2 #_ #_ #H
  38   elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #_ #_ #H destruct
  39 | #a #L #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
  40   elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #H
  41   elim (simple_inv_bind … H)
  42 | #a #L #V2 #V1 #V #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
  43   elim (tshf_inv_flat1 … H) -H #U1 #U2 #_ #H
  44   elim (simple_inv_bind … H)
  45 ]
  46 qed-.