milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / fdeq_fdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma
index 729185985421384618ad585387df1fdae958183d..d337f7054867d39fc3523c11f6b945e6024021ec 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma
@@ -15,37 +15,37 @@
 include "static_2/static/rdeq_rdeq.ma".
 include "static_2/static/fdeq.ma".
 
-(* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
+(* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
 
 (* Advanced properties ******************************************************)
 
-lemma fdeq_sym: ∀h,o. tri_symmetric … (fdeq h o).
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
+lemma fdeq_sym: tri_symmetric … fdeq.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
 /3 width=1 by fdeq_intro_dx, rdeq_sym, tdeq_sym/
 qed-.
 
 (* Main properties **********************************************************)
 
-theorem fdeq_trans: ∀h,o. tri_transitive … (fdeq h o).
-#h #o #G1 #G #L1 #L #T1 #T * -G -L -T
+theorem fdeq_trans: tri_transitive … fdeq.
+#G1 #G #L1 #L #T1 #T * -G -L -T
 #L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
 /4 width=5 by fdeq_intro_sn, rdeq_trans, tdeq_rdeq_div, tdeq_trans/
 qed-.
 
-theorem fdeq_canc_sn: ∀h,o,G,G1,G2,L,L1,L2,T,T1,T2.
-                      â¦\83G, L, Tâ¦\84 â\89\9b[h, o] â¦\83G1, L1, T1â¦\84â\86\92 â¦\83G, L, Tâ¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] ⦃G2, L2, T2⦄.
+theorem fdeq_canc_sn: ∀G,G1,L,L1,T,T1. ⦃G, L, T⦄ ≛ ⦃G1, L1, T1⦄→
+                      â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 â\89\9b â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b ⦃G2, L2, T2⦄.
 /3 width=5 by fdeq_trans, fdeq_sym/ qed-.
 
-theorem fdeq_canc_dx: ∀h,o,G1,G2,G,L1,L2,L,T1,T2,T.
-                      â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G2, L2, T2â¦\84 â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] ⦃G2, L2, T2⦄.
+theorem fdeq_canc_dx: ∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≛ ⦃G, L, T⦄ →
+                      â\88\80G2,L2,T2. â¦\83G2, L2, T2â¦\84 â\89\9b â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b ⦃G2, L2, T2⦄.
 /3 width=5 by fdeq_trans, fdeq_sym/ qed-.
 
 (* Main inversion lemmas with degree-based equivalence on terms *************)
 
-theorem fdeq_tdneq_repl_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
-                            ∀U1,U2. ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄ →
-                            (T2 ≛[h, o] U2 → ⊥) → (T1 ≛[h, o] U1 → ⊥).
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
+theorem fdeq_tdneq_repl_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄ →
+                            ∀U1,U2. ⦃G1, L1, U1⦄ ≛ ⦃G2, L2, U2⦄ →
+                            (T2 ≛ U2 → ⊥) → (T1 ≛ U1 → ⊥).
+#G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
 elim (fdeq_inv_gen_sn … HT) -HT #_ #_ #HT
 elim (fdeq_inv_gen_sn … HU) -HU #_ #_ #HU
 /3 width=5 by tdeq_repl/