matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_eq.ma

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  14
  15 include "delayed_updating/substitution/fsubst.ma".
  16 include "delayed_updating/syntax/prototerm_eq.ma".
  17
  18 (* FOCALIZED SUBSTITUTION ***************************************************)
  19
  20 (* Constructions with subset_equivalence ************************************)
  21
  22 lemma fsubst_empty_rc (t) (u):
  23       u ⇔ t[⋔𝐞←u].
  24 #t #u @conj #p
  25 [ #Hp /3 width=3 by or_introl, ex2_intro/ ]
  26 * *
  27 [ #r #Hr #H0 destruct // ]
  28 #H1p #H2p elim H2p -H2p //
  29 qed.
  30
  31 lemma subset_inclusion_fsubst_bi (t1) (t2) (u1) (u2) (p):
  32       t1 ⊆ t2 → u1 ⊆ u2 → t1[⋔p←u1] ⊆ t2[⋔p←u2].
  33 #t1 #t2 #u1 #u2 #p #Ht #Hu #q * *
  34 [ #r #Hr #H0 destruct
  35   /4 width=3 by ex2_intro, or_introl/
  36 | /4 width=2 by or_intror, conj/
  37 ]
  38 qed.
  39
  40 lemma fsubst_eq_repl (t1) (t2) (u1) (u2) (p1) (p2):
  41       t1 ⇔ t2 → p1 = p2 → u1 ⇔ u2 → t1[⋔p1←u1] ⇔ t2[⋔p2←u2].
  42 #t1 #t2 #u1 #u2 #p1 #p2 * #H1t #H2t #Hp * #H1u #H2u
  43 /3 width=5 by conj, subset_inclusion_fsubst_bi/
  44 qed.