matita/matita/contribs/lambdadelta/delayed_updating/etc/lift/fsubst_eq.etc

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  14
  15 include "delayed_updating/substitution/fsubst.ma".
  16 include "delayed_updating/syntax/prototerm_equivalence.ma".
  17
  18 (* Constructions with subset_equivalence ************************************)
  19
  20 lemma subset_inclusion_fsubst_bi (t1) (t2) (u1) (u2) (p):
  21       t1 ⊆ t2 → u1 ⊆ u2 → t1[⋔p←u1] ⊆ t2[⋔p←u2].
  22 #t1 #t2 #u1 #u2 #p #Ht #Hu #q * *
  23 [ #r #Hr #H0 destruct
  24   /4 width=3 by ex2_intro, or_introl/
  25 | /4 width=2 by or_intror, conj/
  26 ]
  27 qed.
  28
  29 lemma fsubst_eq_repl (t1) (t2) (u1) (u2) (p):
  30       t1 ⇔ t2 → u1 ⇔ u2 → t1[⋔p←u1] ⇔ t2[⋔p←u2].
  31 #t1 #t2 #u1 #u2 #p * #H1t #H2t * #H1u #H2u
  32 /3 width=5 by conj, subset_inclusion_fsubst_bi/
  33 qed.