update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / seq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
index 60830fa46b9772a30102d5afa67f777ea035da24..f928bda7c0bd5e899ff0698df0cf15c5bda060dc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/seq.ma
@@ -13,13 +13,14 @@
 (**************************************************************************)
 
 include "static_2/notation/relations/ideqsn_3.ma".
-include "static_2/syntax/ceq_ext.ma".
+include "static_2/syntax/teq_ext.ma".
 include "static_2/relocation/sex.ma".
 
 (* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
 
 (* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *)
-definition seq: relation3 rtmap lenv lenv ≝ sex ceq_ext cfull.
+definition seq: relation3 rtmap lenv lenv ≝
+           sex ceq_ext cfull.
 
 interpretation
   "syntactic equivalence on selected entries (local environment)"
@@ -27,75 +28,89 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma seq_eq_repl_back: ∀L1,L2. eq_repl_back … (λf. L1 ≡[f] L2).
+lemma seq_eq_repl_back:
+      ∀L1,L2. eq_repl_back … (λf. L1 ≡[f] L2).
 /2 width=3 by sex_eq_repl_back/ qed-.
 
-lemma seq_eq_repl_fwd: ∀L1,L2. eq_repl_fwd … (λf. L1 ≡[f] L2).
+lemma seq_eq_repl_fwd:
+      ∀L1,L2. eq_repl_fwd … (λf. L1 ≡[f] L2).
 /2 width=3 by sex_eq_repl_fwd/ qed-.
 
-lemma sle_seq_trans: ∀f2,L1,L2. L1 ≡[f2] L2 →
-                     ∀f1. f1 ⊆ f2 → L1 ≡[f1] L2.
+lemma sle_seq_trans:
+      ∀f2,L1,L2. L1 ≡[f2] L2 →
+      ∀f1. f1 ⊆ f2 → L1 ≡[f1] L2.
 /2 width=3 by sle_sex_trans/ qed-.
 
 (* Basic_2A1: includes: lreq_refl *)
-lemma seq_refl: ∀f. reflexive … (seq f).
+lemma seq_refl (f):
+      reflexive … (seq f).
 /2 width=1 by sex_refl/ qed.
 
 (* Basic_2A1: includes: lreq_sym *)
-lemma seq_sym: ∀f. symmetric … (seq f).
-/3 width=2 by sex_sym, cext2_sym/ qed-.
+lemma seq_sym (f):
+      symmetric … (seq f).
+/3 width=1 by sex_sym, ceq_ext_sym/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: includes: lreq_inv_atom1 *)
-lemma seq_inv_atom1: ∀f,Y. ⋆ ≡[f] Y → Y = ⋆.
+lemma seq_inv_atom1 (f):
+      ∀Y. ⋆ ≡[f] Y → Y = ⋆.
 /2 width=4 by sex_inv_atom1/ qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair1 *)
-lemma seq_inv_next1: ∀g,J,K1,Y. K1.ⓘ[J] ≡[↑g] Y →
-                     ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ[J].
+lemma seq_inv_next1 (g):
+      ∀J,K1,Y. K1.ⓘ[J] ≡[↑g] Y →
+      ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ[J].
 #g #J #K1 #Y #H
 elim (sex_inv_next1 … H) -H #Z #K2 #HK12 #H1 #H2 destruct
 <(ceq_ext_inv_eq … H1) -Z /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero1 lreq_inv_succ1 *)
-lemma seq_inv_push1: ∀g,J1,K1,Y. K1.ⓘ[J1] ≡[⫯g] Y →
-                     ∃∃J2,K2. K1 ≡[g] K2 & Y = K2.ⓘ[J2].
+lemma seq_inv_push1 (g):
+      ∀J1,K1,Y. K1.ⓘ[J1] ≡[⫯g] Y →
+      ∃∃J2,K2. K1 ≡[g] K2 & Y = K2.ⓘ[J2].
 #g #J1 #K1 #Y #H elim (sex_inv_push1 … H) -H /2 width=4 by ex2_2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_atom2 *)
-lemma seq_inv_atom2: ∀f,X. X ≡[f] ⋆ → X = ⋆.
+lemma seq_inv_atom2 (f):
+      ∀X. X ≡[f] ⋆ → X = ⋆.
 /2 width=4 by sex_inv_atom2/ qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair2 *)
-lemma seq_inv_next2: ∀g,J,X,K2. X ≡[↑g] K2.ⓘ[J] →
-                     ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ[J].
+lemma seq_inv_next2 (g):
+      ∀J,X,K2. X ≡[↑g] K2.ⓘ[J] →
+      ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ[J].
 #g #J #X #K2 #H
 elim (sex_inv_next2 … H) -H #Z #K1 #HK12 #H1 #H2 destruct
 <(ceq_ext_inv_eq … H1) -J /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero2 lreq_inv_succ2 *)
-lemma seq_inv_push2: ∀g,J2,X,K2. X ≡[⫯g] K2.ⓘ[J2] →
-                     ∃∃J1,K1. K1 ≡[g] K2 & X = K1.ⓘ[J1].
+lemma seq_inv_push2 (g):
+      ∀J2,X,K2. X ≡[⫯g] K2.ⓘ[J2] →
+      ∃∃J1,K1. K1 ≡[g] K2 & X = K1.ⓘ[J1].
 #g #J2 #X #K2 #H elim (sex_inv_push2 … H) -H /2 width=4 by ex2_2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair *)
-lemma seq_inv_next: ∀f,I1,I2,L1,L2. L1.ⓘ[I1] ≡[↑f] L2.ⓘ[I2] →
-                    ∧∧ L1 ≡[f] L2 & I1 = I2.
+lemma seq_inv_next (f):
+      ∀I1,I2,L1,L2. L1.ⓘ[I1] ≡[↑f] L2.ⓘ[I2] →
+      ∧∧ L1 ≡[f] L2 & I1 = I2.
 #f #I1 #I2 #L1 #L2 #H elim (sex_inv_next … H) -H
 /3 width=3 by ceq_ext_inv_eq, conj/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_succ *)
-lemma seq_inv_push: ∀f,I1,I2,L1,L2. L1.ⓘ[I1] ≡[⫯f] L2.ⓘ[I2] → L1 ≡[f] L2.
+lemma seq_inv_push (f):
+      ∀I1,I2,L1,L2. L1.ⓘ[I1] ≡[⫯f] L2.ⓘ[I2] → L1 ≡[f] L2.
 #f #I1 #I2 #L1 #L2 #H elim (sex_inv_push … H) -H /2 width=1 by conj/
 qed-.
 
-lemma seq_inv_tl: ∀f,I,L1,L2. L1 ≡[⫱f] L2 → L1.ⓘ[I] ≡[f] L2.ⓘ[I].
+lemma seq_inv_tl (f):
+      ∀I,L1,L2. L1 ≡[⫱f] L2 → L1.ⓘ[I] ≡[f] L2.ⓘ[I].
 /2 width=1 by sex_inv_tl/ qed-.
 
 (* Basic_2A1: removed theorems 5: