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

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  14
  15 include "basic_2/static/ssta_ltpss_dx.ma".
  16 include "basic_2/unwind/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
  19
  20 (* Properties about dx parallel unfold **************************************)
  21
  22 lemma sstas_ltpss_dx_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_dx … H) -T1 /2 width=3/
  28 #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL12 #T #HT0
  29 elim (ssta_ltpss_dx_tpss_conf … HTU0 … HL12 … HT0) -HTU0 -HT0 #U #HTU #HU0
  30 elim (IHU01 … HL12 … HU0) -IHU01 -HL12 -U0 /3 width=4/
  31 qed.
  32
  33 lemma sstas_ltpss_dx_tps_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  34                                ∀L2,d,e. L1 ▶* [d, e] L2 →
  35                                ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
  36                                ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L2 ⊢ U1 ▶* [d, e] U2.
  37 /3 width=7 by step, sstas_ltpss_dx_tpss_conf/ qed. (**) (* auto fails without trace *)
  38
  39 lemma sstas_ltpss_dx_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 →
  40                            ∀L2,d,e. L1 ▶* [d, e] L2 →
  41                            ∃∃U2. ⦃h, L2⦄ ⊢ T •*[g] U2 & L2 ⊢ U1 ▶* [d, e] U2.
  42 /2 width=5/ qed.
  43
  44 lemma sstas_tpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
  45                        ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 →
  46                        ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.
  47 /2 width=5/ qed.
  48
  49 lemma sstas_tps_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
  50                       ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 →
  51                       ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.
  52 /2 width=5/ qed.