λδ-2B is released

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpr_lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
index 312265d54c13701eea6d91375254667e1ac95a3d..dcbe44401f1a76ba9f3f7c41e0b80c30ea7b4948 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
@@ -33,10 +33,10 @@ fact cpr_conf_lpr_atom_atom (h):
 
 fact cpr_conf_lpr_atom_delta (h):
    ∀G0,L0,i. (
-      â\88\80G,L,T. â¦\83G0,L0,#iâ¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,#iâ¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80K0,V0. â¬\87*[i] L0 ≘ K0.ⓓV0 →
-   â\88\80V2. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80T2. â¬\86*[↑i] V2 ≘ T2 →
+   â\88\80K0,V0. â\87©*[i] L0 ≘ K0.ⓓV0 →
+   â\88\80V2. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80T2. â\87§*[↑i] V2 ≘ T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ #i ➡[h] T & ⦃G0,L2⦄ ⊢ T2 ➡[h] T.
 #h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
@@ -54,12 +54,12 @@ qed-.
 (* Basic_1: includes: pr0_delta_delta pr2_delta_delta *)
 fact cpr_conf_lpr_delta_delta (h):
    ∀G0,L0,i. (
-      â\88\80G,L,T. â¦\83G0,L0,#iâ¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,#iâ¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80K0,V0. â¬\87*[i] L0 ≘ K0.ⓓV0 →
-   â\88\80V1. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80T1. â¬\86*[↑i] V1 ≘ T1 →
-   â\88\80KX,VX. â¬\87*[i] L0 ≘ KX.ⓓVX →
-   â\88\80V2. â¦\83G0,KXâ¦\84 â\8a¢ VX â\9e¡[h] V2 â\86\92 â\88\80T2. â¬\86*[↑i] V2 ≘ T2 →
+   â\88\80K0,V0. â\87©*[i] L0 ≘ K0.ⓓV0 →
+   â\88\80V1. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80T1. â\87§*[↑i] V1 ≘ T1 →
+   â\88\80KX,VX. â\87©*[i] L0 ≘ KX.ⓓVX →
+   â\88\80V2. â¦\83G0,KXâ¦\84 â\8a¢ VX â\9e¡[h] V2 â\86\92 â\88\80T2. â\87§*[↑i] V2 ≘ T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ T1 ➡[h] T & ⦃G0,L2⦄ ⊢ T2 ➡[h] T.
 #h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V1 #HV01 #T1 #HVT1
@@ -79,7 +79,7 @@ qed-.
 
 fact cpr_conf_lpr_bind_bind (h):
    ∀p,I,G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\91{p,I}V0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\91{p,I}V0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0.ⓑ{I}V0⦄ ⊢ T0 ➡[h] T1 →
    ∀V2. ⦃G0,L0⦄ ⊢ V0 ➡[h] V2 → ∀T2. ⦃G0,L0.ⓑ{I}V0⦄ ⊢ T0 ➡[h] T2 →
@@ -94,10 +94,10 @@ qed-.
 
 fact cpr_conf_lpr_bind_zeta (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,+â\93\93V0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,+â\93\93V0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0.ⓓV0⦄ ⊢ T0 ➡[h] T1 →
-   â\88\80T2. â¬\86*[1]T2 â\89\98 T0 â\86\92 â\88\80X2. â¦\83G0,L0â¦\84 â\8a¢ T2 â\9e¡[h] X2 â\86\92  
+   â\88\80T2. â\87§*[1]T2 â\89\98 T0 â\86\92 â\88\80X2. â¦\83G0,L0â¦\84 â\8a¢ T2 â\9e¡[h] X2 â\86\92
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ +ⓓV1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ X2 ➡[h] T.
 #h #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
@@ -109,10 +109,10 @@ qed-.
 
 fact cpr_conf_lpr_zeta_zeta (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,+â\93\93V0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,+â\93\93V0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80T1. â¬\86*[1] T1 ≘ T0 → ∀X1. ⦃G0,L0⦄ ⊢ T1 ➡[h] X1 →
-   â\88\80T2. â¬\86*[1] T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
+   â\88\80T1. â\87§*[1] T1 ≘ T0 → ∀X1. ⦃G0,L0⦄ ⊢ T1 ➡[h] X1 →
+   â\88\80T2. â\87§*[1] T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ X1 ➡[h] T & ⦃G0,L2⦄ ⊢ X2 ➡[h] T.
 #h #G0 #L0 #V0 #T0 #IH #T1 #HT10 #X1 #HTX1
@@ -124,7 +124,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_flat (h):
    ∀I,G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\95{I}V0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\95{I}V0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0⦄ ⊢ T0 ➡[h] T1 →
    ∀V2. ⦃G0,L0⦄ ⊢ V0 ➡[h] V2 → ∀T2. ⦃G0,L0⦄ ⊢ T0 ➡[h] T2 →
@@ -139,7 +139,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_eps (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\9dV0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\9dV0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1,T1. ⦃G0,L0⦄ ⊢ T0 ➡[h] T1 → ∀T2. ⦃G0,L0⦄ ⊢ T0 ➡[h] T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
@@ -152,7 +152,7 @@ qed-.
 
 fact cpr_conf_lpr_eps_eps (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\9dV0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\9dV0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀T1. ⦃G0,L0⦄ ⊢ T0 ➡[h] T1 → ∀T2. ⦃G0,L0⦄ ⊢ T0 ➡[h] T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
@@ -165,7 +165,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_beta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\9b{p}W0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\9b{p}W0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0⦄ ⊢ ⓛ{p}W0.T0 ➡[h] T1 →
    ∀V2. ⦃G0,L0⦄ ⊢ V0 ➡[h] V2 → ∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓛW0⦄ ⊢ T0 ➡[h] T2 →
@@ -187,10 +187,10 @@ qed-.
 *)
 fact cpr_conf_lpr_flat_theta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\93{p}W0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\93{p}W0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0⦄ ⊢ ⓓ{p}W0.T0 ➡[h] T1 →
-   â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â¬\86*[1] V2 ≘ U2 →
+   â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â\87§*[1] V2 ≘ U2 →
    ∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ ⓐV1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡[h] T.
@@ -212,7 +212,7 @@ qed-.
 
 fact cpr_conf_lpr_beta_beta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\9b{p}W0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\9b{p}W0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀W1. ⦃G0,L0⦄ ⊢ W0 ➡[h] W1 → ∀T1. ⦃G0,L0.ⓛW0⦄ ⊢ T0 ➡[h] T1 →
    ∀V2. ⦃G0,L0⦄ ⊢ V0 ➡[h] V2 → ∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓛW0⦄ ⊢ T0 ➡[h] T2 →
@@ -231,11 +231,11 @@ qed-.
 (* Basic_1: was: pr0_upsilon_upsilon *)
 fact cpr_conf_lpr_theta_theta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\93{p}W0.T0â¦\84 â\8a\90+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â¦\83G0,L0,â\93\90V0.â\93\93{p}W0.T0â¦\84 â¬\82+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80U1. â¬\86*[1] V1 ≘ U1 →
+   â\88\80V1. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80U1. â\87§*[1] V1 ≘ U1 →
    ∀W1. ⦃G0,L0⦄ ⊢ W0 ➡[h] W1 → ∀T1. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T1 →
-   â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â¬\86*[1] V2 ≘ U2 →
+   â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â\87§*[1] V2 ≘ U2 →
    ∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ ⓓ{p}W1.ⓐU1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡[h] T.