matita/matita/contribs/lambdadelta/basic_2/static/lsubss_ssta.ma

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  14
  15 include "basic_2/static/ssta_lift.ma".
  16 include "basic_2/static/ssta_ssta.ma".
  17 include "basic_2/static/lsubss_ldrop.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED STATIC TYPE ASSIGNMENT *******)
  20
  21 (* Properties concerning stratified native type assignment ******************)
  22
  23 lemma lsubss_ssta_trans: ∀h,g,L2,T,U,l. ⦃h, L2⦄ ⊢ T •[g,l] U →
  24                          ∀L1. h ⊢ L1 •⊑[g] L2 → ⦃h, L1⦄ ⊢ T •[g,l] U.
  25 #h #g #L2 #T #U #l #H elim H -L2 -T -U -l
  26 [ /2 width=1/
  27 | #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
  28   elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  29   elim (lsubss_inv_pair2 … H) -H * #K1 [ | -HWU2 -IHVW2 -HLK1 ]
  30   [ #HK12 #H destruct /3 width=6/
  31   | #V1 #l0 #_ #_ #_ #_ #H destruct
  32   ]
  33 | #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #HWV2 #HWU2 #IHWV2 #L1 #HL12
  34   elim (lsubss_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  35   elim (lsubss_inv_pair2 … H) -H * #K1 [ -HWV2 | -IHWV2 ]
  36   [ #HK12 #H destruct /3 width=6/
  37   | #V1 #l0 #H1 #H2 #_ #H #_ destruct
  38     elim (ssta_fwd_correct … H2) -H2 #V #H
  39     elim (ssta_mono … HWV2 … H) -HWV2 -H /2 width=6/
  40   ]
  41 | /4 width=1/
  42 | /3 width=1/
  43 | /3 width=1/
  44 ]
  45 qed.
  46
  47 lemma lsubss_ssta_conf: ∀h,g,L1,T,U,l. ⦃h, L1⦄ ⊢ T •[g,l] U →
  48                         ∀L2. h ⊢ L1 •⊑[g] L2 → ⦃h, L2⦄ ⊢ T •[g,l] U.
  49 #h #g #L1 #T #U #l #H elim H -L1 -T -U -l
  50 [ /2 width=1/
  51 | #L1 #K1 #V1 #W1 #U1 #i #l #HLK1 #HVW1 #HWU1 #IHVW1 #L2 #HL12
  52   elim (lsubss_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
  53   elim (lsubss_inv_pair1 … H) -H * #K2 [ -HVW1 | -IHVW1 ]
  54   [ #HK12 #H destruct /3 width=6/
  55   | #V2 #l0 #H1 #H2 #_ #H #_ destruct
  56     elim (ssta_mono … HVW1 … H1) -HVW1 -H1 #H1 #H2 destruct
  57     elim (ssta_fwd_correct … H2) -H2 /2 width=6/
  58   ]
  59 | #L1 #K1 #W1 #V1 #U1 #i #l #HLK1 #_ #HWU1 #IHWV1 #L2 #HL12
  60   elim (lsubss_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
  61   elim (lsubss_inv_pair1 … H) -H * #K2 [ | -HWU1 -IHWV1 -HLK2 ]
  62   [ #HK12 #H destruct /3 width=6/
  63   | #V2 #l0 #_ #_ #_ #_ #H destruct
  64   ]
  65 | /4 width=1/
  66 | /3 width=1/
  67 | /3 width=1/
  68 ]
  69 qed.