matita/matita/contribs/lambdadelta/basic_2A/etc/lsubr/sstas_lpss.etc

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  14
  15 include "basic_2/static/ssta_lpss.ma".
  16 include "basic_2/unfold/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
  19
  20 (* Properties about sn parallel substitution for local environments *********)
  21
  22 lemma sstas_cpss_lpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  23                             ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 →
  24                             ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ▶* U2.
  25 #h #g #L1 #T1 #U1 #H @(sstas_ind_dx … H) -T1 /2 width=3/
  26 #T0 #U0 #l0 #HTU0 #_ #IHU01 #T #HT0 #L2 #HL12
  27 elim (ssta_cpss_lpss_conf … HTU0 … HT0 … HL12) -HTU0 -HT0 #U #HTU #HU0
  28 elim (IHU01 … HU0 … HL12) -IHU01 -U0 -HL12 /3 width=4/
  29 qed-.
  30
  31 lemma sstas_cpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
  32                        ∀T2. L ⊢ T1 ▶* T2 →
  33                        ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* U2.
  34 /2 width=3 by sstas_cpss_lpss_conf/ qed-.
  35
  36 lemma sstas_lpss_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 →
  37                        ∀L2. L1 ⊢ ▶* L2 →
  38                        ∃∃U2. ⦃h, L2⦄ ⊢ T •*[g] U2 & L1 ⊢ U1 ▶* U2.
  39 /2 width=3 by sstas_cpss_lpss_conf/ qed-.