- the trace is explicit in all auto tactics with depth > 1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / gget_gget.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/gget_gget.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/gget_gget.ma
index bf14f9e44877c5f9cf97201f9ea71ea7c102e13e..7bd39f09b33a5fea8f10bd4d9b6a912fe17ab7a1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/gget_gget.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/gget_gget.ma
@@ -18,23 +18,23 @@ include "basic_2/substitution/gget.ma".
 
 (* Main properties **********************************************************)
 
-theorem gget_mono: ∀G,G1,e. ⬇[e] G ≡ G1 → ∀G2. ⬇[e] G ≡ G2 → G1 = G2.
-#G #G1 #e #H elim H -G -G1
-[ #G #He #G2 #H
-  >(gget_inv_gt … H He) -H -He //
-| #G #He #G2 #H
-  >(gget_inv_eq … H He) -H -He //
-| #I #G #G1 #V #He #_ #IHG1 #G2 #H
-  lapply (gget_inv_lt … H He) -H -He /2 width=1/
+theorem gget_mono: ∀G,G1,m. ⬇[m] G ≡ G1 → ∀G2. ⬇[m] G ≡ G2 → G1 = G2.
+#G #G1 #m #H elim H -G -G1
+[ #G #Hm #G2 #H
+  >(gget_inv_gt … H Hm) -H -Hm //
+| #G #Hm #G2 #H
+  >(gget_inv_eq … H Hm) -H -Hm //
+| #I #G #G1 #V #Hm #_ #IHG1 #G2 #H
+  lapply (gget_inv_lt … H Hm) -H -Hm /2 width=1 by/
 ]
 qed-.
 
-lemma gget_dec: ∀G1,G2,e. Decidable (⬇[e] G1 ≡ G2).
-#G1 #G2 #e
-elim (gget_total e G1) #G #HG1
+lemma gget_dec: ∀G1,G2,m. Decidable (⬇[m] G1 ≡ G2).
+#G1 #G2 #m
+elim (gget_total m G1) #G #HG1
 elim (eq_genv_dec G G2) #HG2
-[ destruct /2 width=1/
+[ destruct /2 width=1 by or_introl/
 | @or_intror #HG12
-  lapply (gget_mono … HG1 … HG12) -HG1 -HG12 /2 width=1/
+  lapply (gget_mono … HG1 … HG12) -HG1 -HG12 /2 width=1 by/
 ]
 qed-.