matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/sstas_ltpss.etc

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  14
  15 include "basic_2/static/ssta_ltpss.ma".
  16 include "basic_2/unwind/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
  19
  20 (* Properties about parallel unfold *****************************************)
  21
  22 lemma sstas_ltpss_tpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  23                              ∀L2,d,e. L1 ▶* [d, e] L2 →
  24                              ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
  25                              ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 &
  26                                    L2 ⊢ U1 ▶* [d, e] U2.
  27 #h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
  28 [ #T1 #HUT1 #L2 #d #e #HL12 #U2 #HU12
  29   elim (ssta_ltpss_tpss_conf … HUT1 … HL12 … HU12) -HUT1 -HL12 /3 width=3/
  30 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL12 #T #HT0
  31   elim (ssta_ltpss_tpss_conf … HTU0 … HL12 … HT0) -HTU0 -HT0 #U #HTU #HU0
  32   elim (IHU01 … HL12 … HU0) -IHU01 -HL12 -U0 /3 width=4/
  33 ]
  34 qed.
  35
  36 lemma sstas_ltpss_tps_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 & L2 ⊢ U1 ▶* [d, e] U2.
  40 /3 width=5/ qed.
  41
  42 lemma sstas_ltpss_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 →
  43                         ∀L2,d,e. L1 ▶* [d, e] L2 →
  44                         ∃∃U2. ⦃h, L2⦄ ⊢ T •*[g] U2 & L2 ⊢ U1 ▶* [d, e] U2.
  45 /2 width=5/ qed.
  46
  47 lemma sstas_tpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
  48                        ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 →
  49                        ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.
  50 /2 width=5/ qed.
  51
  52 lemma sstas_tps_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
  53                       ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 →
  54                       ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.
  55 /2 width=5/ qed.