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

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  14
  15 include "basic_2/equivalence/lsubss.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED STATIC TYPE ASSIGNMENT *******)
  18
  19 (* Properties concerning basic local environment slicing ********************)
  20
  21 (* Note: the constant 0 cannot be generalized *)
  22 lemma lsubss_ldrop_O1_conf: ∀h,g,L1,L2. h ⊢ L1 •⊑[g] L2 →
  23                             ∀K1,e. ⇩[0, e] L1 ≡ K1 →
  24                             ∃∃K2. h ⊢ K1 •⊑[g] K2 & ⇩[0, e] L2 ≡ K2.
  25 #h #g #L1 #L2 #H elim H -L1 -L2
  26 [ /2 width=3/
  27 | #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
  28   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
  29   [ destruct
  30     elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
  31     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
  32   | elim (IHL12 … HLK1) -L1 /3 width=3/
  33   ]
  34 | #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K1 #e #H
  35   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
  36   [ destruct
  37     elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
  38     <(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
  39   | elim (IHL12 … HLK1) -L1 /3 width=3/
  40   ]
  41 ]
  42 qed-.
  43
  44 (* Note: the constant 0 cannot be generalized *)
  45 lemma lsubss_ldrop_O1_trans: ∀h,g,L1,L2. h ⊢ L1 •⊑[g] L2 →
  46                              ∀K2,e. ⇩[0, e] L2 ≡ K2 →
  47                              ∃∃K1. h ⊢ K1 •⊑[g] K2 & ⇩[0, e] L1 ≡ K1.
  48 #h #g #L1 #L2 #H elim H -L1 -L2
  49 [ /2 width=3/
  50 | #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
  51   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
  52   [ destruct
  53     elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
  54     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
  55   | elim (IHL12 … HLK2) -L2 /3 width=3/
  56   ]
  57 | #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K2 #e #H
  58   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
  59   [ destruct
  60     elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
  61     <(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
  62   | elim (IHL12 … HLK2) -L2 /3 width=3/
  63   ]
  64 ]
  65 qed-.