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 subset_inclusion_fsubst_bi (t1) (t2) (u1) (u2) (p):
  23       t1 ⊆ t2 → u1 ⊆ u2 → t1[⋔p←u1] ⊆ t2[⋔p←u2].
  24 #t1 #t2 #u1 #u2 #p #Ht #Hu #q * *
  25 [ #r #Hr #H0 destruct
  26   /4 width=3 by ex2_intro, or_introl/
  27 | /4 width=2 by or_intror, conj/
  28 ]
  29 qed.
  30
  31 lemma fsubst_eq_repl (t1) (t2) (u1) (u2) (p1) (p2):
  32       t1 ⇔ t2 → p1 = p2 → u1 ⇔ u2 → t1[⋔p1←u1] ⇔ t2[⋔p2←u2].
  33 #t1 #t2 #u1 #u2 #p1 #p2 * #H1t #H2t #Hp * #H1u #H2u
  34 /3 width=5 by conj, subset_inclusion_fsubst_bi/
  35 qed.