matita/matita/contribs/lambdadelta/basic_2/etc/lsubss/lsubss_ssta.etc

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  14
  15 include "basic_2/static/ssta_ssta.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/equivalence/lsubss_ldrop.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED STATIC TYPE ASSIGNMENT *******)
  20
  21 (* Properties on stratified native type assignment **************************)
  22
  23 lemma lsubss_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ →
  24                          ∀L1. h ⊢ L1 •⊑[g] L2 →
  25                          ∃∃U1. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ & L1 ⊢ U1 ⬌* U2.
  26 #h #g #L2 #T #U #l #H elim H -L2 -T -U -l
  27 [ /3 width=3/
  28 | #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
  29   elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  30   elim (lsubss_inv_pair2 … H) -H * #K1 [ | -HWU2 -IHVW2 -HLK1 ]
  31   [ #HK12 #H destruct
  32     elim (IHVW2 … HK12) -K2 #T2 #HVT2 #HTW2
  33     lapply (ldrop_fwd_ldrop2 … HLK1) #H
  34     elim (lift_total T2 0 (i+1)) /3 width=11/
  35   | #W1 #V1 #W2 #l0 #_ #_ #_ #_ #_ #H destruct
  36   ]
  37 | #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #HWV2 #HWU2 #IHWV2 #L1 #HL12
  38   elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  39   elim (lsubss_inv_pair2 … H) -H * #K1 [ -HWV2 | -IHWV2 ]
  40   [ #HK12 #H destruct
  41     elim (IHWV2 … HK12) -K2 /3 width=6/
  42   | #W1 #V1 #T2 #l0 #HVW1 #HWT2 #HW12 #_ #H #_ destruct
  43     elim (ssta_mono … HWV2 … HWT2) -HWV2 -HWT2 #H1 #H2 destruct
  44     lapply (ldrop_fwd_ldrop2 … HLK1) #H
  45     elim (lift_total W1 0 (i+1)) /3 width=11/
  46   ]
  47 | #a #I #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  48   elim (IHTU2 (L1.ⓑ{I}V2) …) [2: /2 width=1/ ] -L2 /3 width=3/
  49 | #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  50   elim (IHTU2 … HL12) -L2 /3 width=5/
  51 | #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  52   elim (IHTU2 … HL12) -L2 /3 width=3/
  53 ]
  54 qed-.