renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / s_computation / fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma
index 808164b69c8f9c445634073b1ffa285fd3f0cdb4..a30e03a457e15b476628f30dd6fe1bcea864f5ad 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma
@@ -12,64 +12,74 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/lib/star.ma".
 include "basic_2/notation/relations/suptermplus_6.ma".
+include "basic_2/notation/relations/suptermplus_7.ma".
 include "basic_2/s_transition/fqu.ma".
 
 (* PLUS-ITERATED SUPCLOSURE *************************************************)
 
-definition fqup: tri_relation genv lenv term ≝ tri_TC … fqu.
+definition fqup: bool → tri_relation genv lenv term ≝
+                 λb. tri_TC … (fqu b).
+
+interpretation "extended plus-iterated structural successor (closure)"
+   'SupTermPlus b G1 L1 T1 G2 L2 T2 = (fqup b G1 L1 T1 G2 L2 T2).
 
 interpretation "plus-iterated structural successor (closure)"
-   'SupTermPlus G1 L1 T1 G2 L2 T2 = (fqup G1 L1 T1 G2 L2 T2).
+   'SupTermPlus G1 L1 T1 G2 L2 T2 = (fqup true G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fqu_fqup: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
+lemma fqu_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+                ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
 /2 width=1 by tri_inj/ qed.
 
-lemma fqup_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2.
-                   ⦃G1, L1, T1⦄ ⊐+ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐ ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
+lemma fqup_strap1: ∀b,G1,G,G2,L1,L,L2,T1,T,T2.
+                   ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+                   ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
 /2 width=5 by tri_step/ qed.
 
-lemma fqup_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2.
-                   ⦃G1, L1, T1⦄ ⊐ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄.
+lemma fqup_strap2: ∀b,G1,G,G2,L1,L,L2,T1,T,T2.
+                   ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
+                   ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
 /2 width=5 by tri_TC_strap/ qed.
 
-lemma fqup_pair_sn: ∀I,G,L,V,T. ⦃G, L, ②{I}V.T⦄ ⊐+ ⦃G, L, V⦄.
+lemma fqup_pair_sn: ∀b,I,G,L,V,T. ⦃G, L, ②{I}V.T⦄ ⊐+[b] ⦃G, L, V⦄.
 /2 width=1 by fqu_pair_sn, fqu_fqup/ qed.
 
-lemma fqup_bind_dx: ∀a,I,G,L,V,T. ⦃G, L, ⓑ{a,I}V.T⦄ ⊐+ ⦃G, L.ⓑ{I}V, T⦄.
+lemma fqup_bind_dx: ∀b,p,I,G,L,V,T. ⦃G, L, ⓑ{p,I}V.T⦄ ⊐+[b] ⦃G, L.ⓑ{I}V, T⦄.
 /2 width=1 by fqu_bind_dx, fqu_fqup/ qed.
 
-lemma fqup_flat_dx: ∀I,G,L,V,T. ⦃G, L, ⓕ{I}V.T⦄ ⊐+ ⦃G, L, T⦄.
+lemma fqup_clear: ∀p,I,G,L,V,T. ⦃G, L, ⓑ{p,I}V.T⦄ ⊐+[Ⓕ] ⦃G, L.ⓧ, T⦄.
+/3 width=1 by fqu_clear, fqu_fqup/ qed.
+
+lemma fqup_flat_dx: ∀b,I,G,L,V,T. ⦃G, L, ⓕ{I}V.T⦄ ⊐+[b] ⦃G, L, T⦄.
 /2 width=1 by fqu_flat_dx, fqu_fqup/ qed.
 
-lemma fqup_flat_dx_pair_sn: ∀I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.②{I2}V2.T⦄ ⊐+ ⦃G, L, V2⦄.
+lemma fqup_flat_dx_pair_sn: ∀b,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.②{I2}V2.T⦄ ⊐+[b] ⦃G, L, V2⦄.
 /2 width=5 by fqu_pair_sn, fqup_strap1/ qed.
 
-lemma fqup_bind_dx_flat_dx: ∀a,G,I1,I2,L,V1,V2,T. ⦃G, L, ⓑ{a,I1}V1.ⓕ{I2}V2.T⦄ ⊐+ ⦃G, L.ⓑ{I1}V1, T⦄.
+lemma fqup_bind_dx_flat_dx: ∀b,p,G,I1,I2,L,V1,V2,T. ⦃G, L, ⓑ{p,I1}V1.ⓕ{I2}V2.T⦄ ⊐+[b] ⦃G, L.ⓑ{I1}V1, T⦄.
 /2 width=5 by fqu_flat_dx, fqup_strap1/ qed.
 
-lemma fqup_flat_dx_bind_dx: ∀a,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.ⓑ{a,I2}V2.T⦄ ⊐+ ⦃G, L.ⓑ{I2}V2, T⦄.
+lemma fqup_flat_dx_bind_dx: ∀b,p,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.ⓑ{p,I2}V2.T⦄ ⊐+[b] ⦃G, L.ⓑ{I2}V2, T⦄.
 /2 width=5 by fqu_bind_dx, fqup_strap1/ qed.
 
 (* Basic eliminators ********************************************************)
 
-lemma fqup_ind: ∀G1,L1,T1. ∀R:relation3 ….
-                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → R G2 L2 T2.
-#G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
+lemma fqup_ind: ∀b,G1,L1,T1. ∀Q:relation3 ….
+                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G L T → Q G2 L2 T2) →
+                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
+#b #G1 #L1 #T1 #Q #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
 qed-.
 
-lemma fqup_ind_dx: ∀G2,L2,T2. ∀R:relation3 ….
-                   (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → R G1 L1 T1) →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+ ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → R G1 L1 T1.
-#G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
+lemma fqup_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 ….
+                   (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1) →
+                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G L T → Q G1 L1 T1) →
+                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1.
+#b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
 qed-.