partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / fsle_fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
index 04162cc187ec15f653124e1d99597ac2c9e727cf..c49ebe63da3cc3ac04532974a51ad3b20f0f00cc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fqup.ma
@@ -22,68 +22,68 @@ include "static_2/static/fsle_length.ma".
 lemma fsle_refl: bi_reflexive … fsle.
 #L #T
 elim (frees_total L T) #f #Hf
-/2 width=8 by sle_refl, ex4_4_intro/
+/2 width=8 by pr_sle_refl, ex4_4_intro/
 qed.
 
 lemma fsle_shift: ∀L1,L2. |L1| = |L2| →
-                  â\88\80I,T1,T2,V.  â¦\83L1.â\93§,T1â¦\84 â\8a\86 â¦\83L2.â\93\91{I}V,T2â¦\84 →
-                  â\88\80p. â¦\83L1.â\93§,T1â¦\84 â\8a\86 â¦\83L2,â\93\91{p,I}V.T2â¦\84.
+                  â\88\80I,T1,T2,V.  â\9dªL1.â\93§,T1â\9d« â\8a\86 â\9dªL2.â\93\91[I]V,T2â\9d« →
+                  â\88\80p. â\9dªL1.â\93§,T1â\9d« â\8a\86 â\9dªL2,â\93\91[p,I]V.T2â\9d«.
 #L1 #L2 #H1L #I #T1 #T2 #V
 * #n #m #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
 elim (lveq_inj_length … H2L) // -H1L #H1 #H2 destruct
-lapply (lveq_inv_bind … H2L) -H2L #HL
+lapply (lveq_inv_bind_O … H2L) -H2L #HL
 elim (frees_total L2 V) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-lapply (sor_inv_sle_dx … Hg) #H0g
-/4 width=10 by frees_bind, lveq_void_sn, sle_tl, sle_trans, ex4_4_intro/
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+lapply (pr_sor_inv_sle_dx … Hg) #H0g
+/4 width=10 by frees_bind, lveq_void_sn, pr_sle_tl, pr_sle_trans, ex4_4_intro/
 qed.
 
-lemma fsle_bind_dx_sn: â\88\80L1,L2,V1,V2. â¦\83L1,V1â¦\84 â\8a\86 â¦\83L2,V2â¦\84 →
-                       â\88\80p,I,T2. â¦\83L1,V1â¦\84 â\8a\86 â¦\83L2,â\93\91{p,I}V2.T2â¦\84.
+lemma fsle_bind_dx_sn: â\88\80L1,L2,V1,V2. â\9dªL1,V1â\9d« â\8a\86 â\9dªL2,V2â\9d« →
+                       â\88\80p,I,T2. â\9dªL1,V1â\9d« â\8a\86 â\9dªL2,â\93\91[p,I]V2.T2â\9d«.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
 elim (frees_total (L2.ⓧ) T2) #g2 #Hg2
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)
-/4 width=5 by frees_bind_void, sor_inv_sle_sn, sor_tls, sle_trans/
+/4 width=5 by frees_bind_void, pr_sor_inv_sle_sn, pr_sor_tls, pr_sle_trans/
 qed.
 
-lemma fsle_bind_dx_dx: â\88\80L1,L2,T1,T2. â¦\83L1,T1â¦\84 â\8a\86 â¦\83L2.â\93§,T2â¦\84 → |L1| ≤ |L2| →
-                       â\88\80p,I,V2. â¦\83L1,T1â¦\84 â\8a\86 â¦\83L2,â\93\91{p,I}V2.T2â¦\84.
+lemma fsle_bind_dx_dx: â\88\80L1,L2,T1,T2. â\9dªL1,T1â\9d« â\8a\86 â\9dªL2.â\93§,T2â\9d« → |L1| ≤ |L2| →
+                       â\88\80p,I,V2. â\9dªL1,T1â\9d« â\8a\86 â\9dªL2,â\93\91[p,I]V2.T2â\9d«.
 #L1 #L2 #T1 #T2 * #n1 #x1 #f2 #g2 #Hf2 #Hg2 #H #Hfg2 #HL12 #p #I #V2
 elim (lveq_inv_void_dx_length … H HL12) -H -HL12 #m1 #HL12 #H1 #H2 destruct
-<tls_xn in Hfg2; #Hfg2
+<pr_tls_swap in Hfg2; #Hfg2
 elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
-/4 width=5 by frees_bind_void, sor_inv_sle_dx, sor_tls, sle_trans/
+/4 width=5 by frees_bind_void, pr_sor_inv_sle_dx, pr_sor_tls, pr_sle_trans/
 qed.
 
-lemma fsle_flat_dx_sn: â\88\80L1,L2,V1,V2. â¦\83L1,V1â¦\84 â\8a\86 â¦\83L2,V2â¦\84 →
-                       â\88\80I,T2. â¦\83L1,V1â¦\84 â\8a\86 â¦\83L2,â\93\95{I}V2.T2â¦\84.
+lemma fsle_flat_dx_sn: â\88\80L1,L2,V1,V2. â\9dªL1,V1â\9d« â\8a\86 â\9dªL2,V2â\9d« →
+                       â\88\80I,T2. â\9dªL1,V1â\9d« â\8a\86 â\9dªL2,â\93\95[I]V2.T2â\9d«.
 #L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #I #T2
 elim (frees_total L2 T2) #g2 #Hg2
-elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+elim (pr_sor_isf_bi g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
 @(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)
-/4 width=5 by frees_flat, sor_inv_sle_sn, sor_tls, sle_trans/
+/4 width=5 by frees_flat, pr_sor_inv_sle_sn, pr_sor_tls, pr_sle_trans/
 qed.
 
-lemma fsle_flat_dx_dx: â\88\80L1,L2,T1,T2. â¦\83L1,T1â¦\84 â\8a\86 â¦\83L2,T2â¦\84 →
-                       â\88\80I,V2. â¦\83L1,T1â¦\84 â\8a\86 â¦\83L2,â\93\95{I}V2.T2â¦\84.
+lemma fsle_flat_dx_dx: â\88\80L1,L2,T1,T2. â\9dªL1,T1â\9d« â\8a\86 â\9dªL2,T2â\9d« →
+                       â\88\80I,V2. â\9dªL1,T1â\9d« â\8a\86 â\9dªL2,â\93\95[I]V2.T2â\9d«.
 #L1 #L2 #T1 #T2 * #n1 #m1 #f2 #g2 #Hf2 #Hg2 #HL12 #Hfg2 #I #V2
 elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
+elim (pr_sor_isf_bi g1 g2) /2 width=3 by frees_fwd_isfin/ #g #Hg #_
 @(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
-/4 width=5 by frees_flat, sor_inv_sle_dx, sor_tls, sle_trans/
+/4 width=5 by frees_flat, pr_sor_inv_sle_dx, pr_sor_tls, pr_sle_trans/
 qed.
 
 (* Advanced forward lemmas ***************************************************)
 
-lemma fsle_fwd_pair_sn: â\88\80I1,I2,L1,L2,V1,V2,T1,T2. â¦\83L1.â\93\91{I1}V1,T1â¦\84 â\8a\86 â¦\83L2.â\93\91{I2}V2,T2â¦\84 →
-                        â¦\83L1.â\93§,T1â¦\84 â\8a\86 â¦\83L2.â\93\91{I2}V2,T2â¦\84.
+lemma fsle_fwd_pair_sn: â\88\80I1,I2,L1,L2,V1,V2,T1,T2. â\9dªL1.â\93\91[I1]V1,T1â\9d« â\8a\86 â\9dªL2.â\93\91[I2]V2,T2â\9d« →
+                        â\9dªL1.â\93§,T1â\9d« â\8a\86 â\9dªL2.â\93\91[I2]V2,T2â\9d«.
 #I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 *
 #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12
 elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
 elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
 lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
-/5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
+/5 width=10 by lsubf_fwd_sle, lveq_bind, pr_sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
 qed-.