matita/matita/contribs/lambdadelta/basic_2/etc/cpr/ssta_ltpss_sn.etc

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  14
  15 include "basic_2/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/static/ssta_ltpss_dx.ma".
  17
  18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
  19
  20 (* Properties about sn parallel unfold **************************************)
  21
  22 lemma ssta_ltpss_sn_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ →
  23                           ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  24                           ∃∃U2. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* [d, e] U2.
  25 #h #g #L1 #T #U1 #l #HTU1 #L2 #d #e #HL12
  26 lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
  27 @(ltpssa_ind … HL12) -L2 [ /2 width=3/ ] -HTU1
  28 #L #L2 #HL1 #HL2 * #U #HTU #HU1
  29 lapply (ltpssa_ltpss_sn … HL1) -HL1 #HL1
  30 elim (ssta_ltpss_dx_conf … HTU … HL2) -HTU #U2 #HTU2 #HU2
  31 lapply (ltpss_dx_tpss_trans_eq … HU2 … HL2) -HU2 -HL2 #HU2
  32 lapply (ltpss_sn_tpss_trans_eq … HU2 … HL1) -HU2 -HL1 #HU2
  33 lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
  34 qed.
  35
  36 lemma ssta_ltpss_sn_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
  37                                ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  38                                ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
  39                                ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ &
  40                                      L1 ⊢ U1 ▶* [d, e] U2.
  41 #h #g #L1 #T1 #U1 #l #HTU1 #L2 #d #e #HL12 #T2 #HT12
  42 elim (ssta_ltpss_sn_conf … HTU1 … HL12) -HTU1 #U #HT1U #HU1
  43 elim (ssta_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 ssta_ltpss_sn_tps_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
  49                               ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  50                               ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
  51                               ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ &
  52                                     L1 ⊢ U1 ▶* [d, e] U2.
  53 /3 width=3/ qed.