update in delayed_updating and ground

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_path_closed.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
index 79443ca3ba9258b36eff07e4a2c27db3ba200865..0c2aa6219efe4b7a219d20d9e363c920bc50d218 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
@@ -20,24 +20,25 @@ include "ground/relocation/xap.ma".
 
 (* Constructions with pcc ***************************************************)
 
-lemma lift_path_closed (f) (q) (n):
-      q ϵ 𝐂❨n❩ → ↑[f]q ϵ 𝐂❨↑[q]f＠❨n❩❩.
-#f #q #n #Hq elim Hq -Hq //
-#q #n [ #k ] #_ #IH
-/2 width=1 by pcc_d_dx, pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
+lemma lift_path_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n❩ → ↑[f]q ϵ 𝐂❨o,↑[q]f＠❨n❩❩.
+#o #f #q #n #H0 elim H0 -q -n //
+#q #n [ #k #Ho ] #_ #IH
+/2 width=1 by pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
+/4 width=1 by pcc_d_dx, tr_xap_pos/
 qed.
 
-lemma lift_path_rmap_closed (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ → ↑[↑[p]f]q ϵ 𝐂❨↑[p●q]f＠❨n❩❩.
+lemma lift_path_rmap_closed (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ → ↑[↑[p]f]q ϵ 𝐂❨o,↑[p●q]f＠❨n❩❩.
 /2 width=1 by lift_path_closed/
 qed.
 
-lemma lift_path_rmap_closed_L (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ → ↑[↑[p◖𝗟]f]q ϵ 𝐂❨↑[p●𝗟◗q]f＠§❨n❩❩.
-#f #p #q #n #Hq
-lapply (lift_path_closed (↑[p◖𝗟]f) … Hq) #Hq0
+lemma lift_path_rmap_closed_L (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ → ↑[↑[p◖𝗟]f]q ϵ 𝐂❨o,↑[p●𝗟◗q]f＠§❨n❩❩.
+#o #f #p #q #n #Hq
+lapply (lift_path_closed … (↑[p◖𝗟]f) … Hq) #Hq0
 lapply (pcc_L_sn … Hq) -Hq #Hq1
-lapply (lift_path_rmap_closed f p … Hq1) -Hq1
+lapply (lift_path_rmap_closed … f p … Hq1) -Hq1
 <lift_path_L_sn >lift_rmap_L_dx #Hq1
 elim (pcc_inv_L_sn … Hq1 Hq0) -Hq1 #H0 #_
 <H0 in Hq0; -H0 //