1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "delayed_updating/substitution/fsubst.ma".
16 include "delayed_updating/syntax/prototerm_equivalence.ma".
18 (* Constructions with subset_equivalence ************************************)
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 * *
24 /4 width=3 by ex2_intro, or_introl/
25 | /4 width=2 by or_intror, conj/
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/