matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/sstas_ltpss_sn.etc

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  14
  15 include "basic_2/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/unwind/sstas_ltpss_dx.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS ************************)
  19
  20 (* Properties about sn parallel unfold *****************************************)
  21
  22 lemma sstas_ltpss_sn_conf: ∀h,g,L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  23                            ∀T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 →
  24                            ∃∃U2. L1 ⊢ U1 ▶* [d, e] U2 & ⦃h, L2⦄ ⊢ T •*[g] U2.
  25 #h #g #L1 #L2 #d #e #H
  26 lapply (ltpss_sn_ltpssa … H) -H #H @(ltpssa_ind … H) -L2 /2 width=3/
  27 #L #L2 #HL1 #HL2 #IHL1 #T #U1 #H1
  28 lapply (ltpssa_ltpss_sn … HL1) -HL1 #HL1
  29 lapply (ltpss_sn_dx_trans_eq … HL1 … HL2) -HL1 #HL12
  30 elim (IHL1 … H1) -IHL1 -H1 #U #HU1 #HTU
  31 elim (sstas_ltpss_dx_conf … HTU … HL2) -HTU -HL2 #U2 #H2 #HU2
  32 lapply (ltpss_sn_tpss_trans_eq … HU2 … HL12) -HU2 -HL12 #HU2
  33 lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
  34 qed.
  35
  36 lemma sstas_ltpss_sn_tpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  37                                 ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  38                                 ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
  39                                 ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 &
  40                                       L1 ⊢ U1 ▶* [d, e] U2.
  41 #h #g #L1 #T1 #U1 #HTU1 #L2 #d #e #HL12 #T2 #HT12
  42 elim (sstas_ltpss_sn_conf … HL12 … HTU1) -HTU1 #U #HU1 #HT1U
  43 elim (sstas_tpss_conf … HT1U … HT12) -T1 #U2 #HTU2 #HU2
  44 lapply (ltpss_sn_tpss_trans_eq … HU2 … HL12) -HU2 -HL12 #HU2
  45 lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
  46 qed.
  47
  48 lemma sstas_ltpss_sn_tps_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  49                                ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  50                                ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
  51                                ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 &
  52                                      L1 ⊢ U1 ▶* [d, e] U2.
  53 /3 width=3/ qed.