X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffrees_frees.ma;h=17e1f983d746086ad6e2cc612245b4e0d6ee885c;hp=4cf172a1c11404c1538e41715b6186f7e4233731;hb=222044da28742b24584549ba86b1805a87def070;hpb=3ef251397627da80aeea0cf08b053a4bc781ef88

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/frees_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/static/frees_frees.ma
index 4cf172a1c..17e1f983d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/frees_frees.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/frees_frees.ma
@@ -18,24 +18,24 @@ include "basic_2/static/frees.ma".
 
 (* Main inversion lemmas ****************************************************)
 
-theorem frees_mono: ∀L,T,f1. L ⊢ 𝐅*⦃T⦄ ≡ f1 → ∀f2. L ⊢ 𝐅*⦃T⦄ ≡ f2 → f1 ≗ f2.
-#L #T #f1 #H elim H -L -T -f1
-[ /3 width=2 by frees_inv_atom, isid_inv_eq_repl/
-| /4 width=5 by frees_inv_sort, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
-| #I #L #V #f1 #_ #IH #x #H elim (frees_inv_zero … H) -H *
-  [ #H destruct
-  | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_next/
-  ]
-| #I #L #V #i #f1 #_ #IH #x #H elim (frees_inv_lref … H) -H *
-  [ #H destruct
-  | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_push/
-  ]
-| /4 width=5 by frees_inv_gref, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
-| #I #L #V #T #p #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_bind … H) -H
-  #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
+theorem frees_mono: ∀f1,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f1 → ∀f2. L ⊢ 𝐅*⦃T⦄ ≘ f2 → f1 ≡ f2.
+#f1 #L #T #H elim H -f1 -L -T
+[ /3 width=3 by frees_inv_sort, isid_inv_eq_repl/
+| #f1 #i #Hf1 #g2 #H
+  elim (frees_inv_atom … H) -H #f2 #Hf2 #H destruct
+  /4 width=5 by isid_inv_eq_repl, pushs_eq_repl, eq_next/
+| #f1 #I #L #V #_ #IH #g2 #H elim (frees_inv_pair … H) -H
+  #f2 #Hf2 #H destruct /3 width=5 by eq_next/
+| #f1 #I #L #Hf1 #g2 #H elim (frees_inv_unit … H) -H
+  #f2 #Hf2 #H destruct /3 width=5 by isid_inv_eq_repl, eq_next/
+| #f1 #I #L #i #_ #IH #g2 #H elim (frees_inv_lref … H) -H
+  #f2 #Hf2 #H destruct /3 width=5 by eq_push/
+| /3 width=3 by frees_inv_gref, isid_inv_eq_repl/
+| #f1V #f1T #f1 #p #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_bind … H) -H
+  #f2V #f2T #HV #HT #Hf2 @(sor_mono … Hf1) -Hf1
   /5 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1, tl_eq_repl/ (**) (* full auto too slow *)
-| #I #L #V #T #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_flat … H) -H
-  #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
+| #f1V #f1T #f1 #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_flat … H) -H
+  #f2V #f2T #HV #HT #Hf2 @(sor_mono … Hf1) -Hf1
   /4 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1/ (**) (* full auto too slow *)
 ]
 qed-.