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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/static/lfxs_lfxs.ma".
16 include "basic_2/static/frees_frees.ma".
18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
20 theorem lfxs_conf: ∀R. R_confluent_lfxs R R R R →
21 ∀T. confluent … (lfxs R T).
22 #R #H1R #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02
23 lapply (frees_mono … Hf1 … Hf) -Hf1 #Hf12
24 lapply (lexs_eq_repl_back … HL01 … Hf12) -f1 #HL01
25 elim (lexs_conf … HL01 … HL02)
27 lemma pippo: ∀R1,R2,RP1,RP2. R_confluent_lfxs R1 R2 RP1 RP2 →
28 lexs_confluent R1 R2 RP1 cfull RP2 cfull.
29 #R1 #R2 #RP1 #RP2 #HR #f #L0 #T0 #T1 #HT01 #T2 #HT02 #L1 #HL01 #L2