matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup_csup.etc

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  14
  15 include "basic_2/substitution/ldrop_ldrop.ma".
  16 include "basic_2/substitution/csup.ma".
  17
  18 (* SUPCLOSURE ***************************************************************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 lemma csup_inv_ldrop: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
  23                       ∀J,W,j. ⇩[0, j] L1 ≡ L2.ⓑ{J}W → T1 = #j ∧ T2 = W.
  24 #L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
  25 [ #I #L #K #V #i #HLKV #J #W #j #HLKW
  26   elim (ldrop_conf_div … HLKV … HLKW) -L /2 width=1/
  27 | #a
  28 | #a
  29 ]
  30 #I #L #V #T #J #W #j #H
  31 lapply (ldrop_pair2_fwd_cw … H W) -H #H
  32 [2: lapply (transitive_lt (#{L,W}) … H) /2 width=1/ -H #H ]
  33 elim (lt_refl_false … H)
  34 qed-.
  35
  36 (* Main forward lemmas ******************************************************)
  37
  38 theorem csup_trans_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
  39                              ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ →
  40                              L = L0 ∨ ⦃L, T1⦄ > ⦃L, T3⦄.
  41 #L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
  42 [ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
  43   lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
  44   lapply (csup_fwd_cw … H) -H #H2
  45   lapply (transitive_lt … H1 H2) -H1 -H2 #H
  46   elim (lt_refl_false … H)
  47 | #a #I #L0 #V2 #T2 #T3 #HT23
  48   elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
  49   qed-.