update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
index 08ff3ebb3af1d19d8a5e47511a1aead4143fec2e..21186fdd65c6bbe0bdf65cd8fcc7ec25352cba76 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -20,12 +20,12 @@ include "delayed_updating/syntax/prototerm_proper.ma".
 
 (* FOCALIZED SUBSTITUTION ***************************************************)
 
-lemma lift_fsubst_sn (f) (t) (u) (p): Ꝕu →
+lemma lift_fsubst_sn (f) (t) (u) (p): u ϵ 𝐏 →
       (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u] ⊆ ↑[f](t[⋔p←u]).
 #f #t #u #p #Hu #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
   >lift_append_proper_dx
-  /4 width=1 by subset_in_ext_f1_dx, or_introl/
+  /4 width=5 by in_comp_lift_bi, in_ppc_comp_trans, or_introl, ex2_intro/
 | * #q #Hq #H1 #H0
   @(ex2_intro … H1) @or_intror @conj // *
   [ <list_append_empty_dx #H2 destruct
@@ -36,15 +36,15 @@ lemma lift_fsubst_sn (f) (t) (u) (p): Ꝕu →
 ]
 qed-.
 
-lemma lift_fsubst_dx (f) (t) (u) (p): Ꝕu → p ϵ ▵t → t ϵ 𝐓 →
+lemma lift_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       ↑[f](t[⋔p←u]) ⊆ (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u].
 #f #t #u #p #Hu #H1p #H2p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
-  [|| <lift_append_proper_dx /2 width=1 by/ ]
+  [|| <lift_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
   /2 width=3 by ex2_intro/
 | #Hq #H0 #H1 destruct
-  @or_intror @conj [ /2 width=1 by subset_in_ext_f1_dx/ ] *
+  @or_intror @conj [ /2 width=1 by in_comp_lift_bi/ ] *
   [ <list_append_empty_dx #Hr @(H0 … (𝐞)) -H0
     <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
   | #l #r #Hr
@@ -54,6 +54,6 @@ lemma lift_fsubst_dx (f) (t) (u) (p): Ꝕu → p ϵ ▵t → t ϵ 𝐓 →
 ]
 qed-.
 
-lemma lift_fsubst (f) (t) (u) (p): Ꝕu → p ϵ ▵t → t ϵ 𝐓 →
+lemma lift_fsubst (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u] ⇔ ↑[f](t[⋔p←u]).
 /4 width=3 by lift_fsubst_sn, conj, lift_fsubst_dx/ qed.