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4 (* ||A|| A project by Andrea Asperti *)
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15 include "delayed_updating/substitution/fsubst.ma".
16 include "delayed_updating/syntax/prototerm_eq.ma".
18 (* FOCALIZED SUBSTITUTION ***************************************************)
20 (* Constructions with subset_equivalence ************************************)
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 * *
26 /4 width=3 by ex2_intro, or_introl/
27 | /4 width=2 by or_intror, conj/
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/