X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_path_closed.ma;h=0c2aa6219efe4b7a219d20d9e363c920bc50d218;hp=79443ca3ba9258b36eff07e4a2c27db3ba200865;hb=d06053844638d88936d711b66fddbcca2a9add1c;hpb=9e31ac1f3f868349154b0ce2e550e2476aaf6a30 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 79443ca3b..0c2aa6219 100644 --- 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_rmap_L_dx #Hq1 elim (pcc_inv_L_sn … Hq1 Hq0) -Hq1 #H0 #_