matita/matita/contribs/lambdadelta/static_2/relocation/drops_seq.ma

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  14
  15 include "static_2/relocation/drops_sex.ma".
  16
  17 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
  18
  19 (* Properties with syntactic equivalence for selected local environments ****)
  20
  21 lemma seq_co_dedropable_sn: co_dedropable_sn seq.
  22 @sex_liftable_co_dedropable_sn
  23 /2 width=6 by cfull_lift_sn, ceq_lift_sn/ qed-.
  24
  25 lemma seq_co_dropable_sn: co_dropable_sn seq.
  26 @sex_co_dropable_sn qed-.
  27
  28 lemma seq_co_dropable_dx: co_dropable_dx seq.
  29 @sex_co_dropable_dx qed-.
  30
  31 (* Basic_2A1: includes: lreq_drop_trans_be *)
  32 lemma seq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
  33                             ∀b,f,I,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} → 𝐔⦃f⦄ →
  34                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
  35                             ∃∃K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} & K1 ≡[f1] K2.
  36 #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
  37 elim (sex_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
  38 #I1 #K1 #HLK1 #HK12 #H <(ceq_ext_inv_eq … H) -I2
  39 /2 width=3 by ex2_intro/
  40 qed-.
  41
  42 (* Basic_2A1: includes: lreq_drop_conf_be *)
  43 lemma seq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
  44                            ∀b,f,I,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} → 𝐔⦃f⦄ →
  45                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
  46                            ∃∃K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} & K1 ≡[f1] K2.
  47 #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
  48 elim (seq_drops_trans_next … (seq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
  49 /3 width=3 by seq_sym, ex2_intro/
  50 qed-.
  51
  52 lemma drops_seq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
  53                             ∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≘ K1 →
  54                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
  55                             ∃∃L2. ⬇*[b, f] L2.ⓘ{I} ≘ K2 & L1 ≡[f2] L2 & L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
  56 #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
  57 elim (drops_sex_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
  58 /2 width=6 by cfull_lift_sn, ceq_lift_sn/
  59 #I2 #L2 #HLK2 #HL12 #H >(ceq_ext_inv_eq … H) -I1
  60 /2 width=4 by ex3_intro/
  61 qed-.