- notational change for cpg and cpx

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_cpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
index 8f77d9190d16e7c9aaf85f6013161a19213bfbd5..4f1d7ceeeb2affcc473c3401c884b5fab1a920ef 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
@@ -22,58 +22,58 @@ include "basic_2/computation/cpxs_lift.ma".
 theorem cpxs_trans: ∀h,o,G,L. Transitive … (cpxs h o G L).
 normalize /2 width=3 by trans_TC/ qed-.
 
-theorem cpxs_bind: â\88\80h,o,a,I,G,L,V1,V2,T1,T2. â¦\83G, L.â\93\91{I}V1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â\9e¡*[h, o] ⓑ{a,I}V2.T2.
+theorem cpxs_bind: â\88\80h,o,a,I,G,L,V1,V2,T1,T2. â¦\83G, L.â\93\91{I}V1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
+                   â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V2 →
+                   â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â¬\88*[h, o] ⓑ{a,I}V2.T2.
 #h #o #a #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_bind_dx/
 qed.
 
-theorem cpxs_flat: â\88\80h,o,I,G,L,V1,V2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â\9e¡*[h, o] ⓕ{I}V2.T2.
+theorem cpxs_flat: â\88\80h,o,I,G,L,V1,V2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
+                   â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V2 →
+                   â¦\83G, Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â¬\88*[h, o] ⓕ{I}V2.T2.
 #h #o #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_flat_dx/
 qed.
 
 theorem cpxs_beta_rc: ∀h,o,a,G,L,V1,V2,W1,W2,T1,T2.
-                      â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, o] V2 â\86\92 â¦\83G, L.â\93\9bW1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â\9e¡*[h, o] W2 →
-                      â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{a}W1.T1 â\9e¡*[h, o] ⓓ{a}ⓝW2.V2.T2.
+                      â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h, o] V2 â\86\92 â¦\83G, L.â\93\9bW1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â¬\88*[h, o] W2 →
+                      â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{a}W1.T1 â¬\88*[h, o] ⓓ{a}ⓝW2.V2.T2.
 #h #o #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2
 /4 width=5 by cpxs_trans, cpxs_beta_dx, cpxs_bind_dx, cpx_pair_sn/
 qed.
 
 theorem cpxs_beta: ∀h,o,a,G,L,V1,V2,W1,W2,T1,T2.
-                   â¦\83G, L.â\93\9bW1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â\9e¡*[h, o] W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V2 →
-                   â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{a}W1.T1 â\9e¡*[h, o] ⓓ{a}ⓝW2.V2.T2.
+                   â¦\83G, L.â\93\9bW1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â¬\88*[h, o] W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V2 →
+                   â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{a}W1.T1 â¬\88*[h, o] ⓓ{a}ⓝW2.V2.T2.
 #h #o #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2
 /4 width=5 by cpxs_trans, cpxs_beta_rc, cpxs_bind_dx, cpx_flat/
 qed.
 
 theorem cpxs_theta_rc: ∀h,o,a,G,L,V1,V,V2,W1,W2,T1,T2.
-                       â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, o] V → ⬆[0, 1] V ≡ V2 →
-                       â¦\83G, L.â\93\93W1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â\9e¡*[h, o] W2 →
-                       â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}W1.T1 â\9e¡*[h, o] ⓓ{a}W2.ⓐV2.T2.
+                       â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h, o] V → ⬆[0, 1] V ≡ V2 →
+                       â¦\83G, L.â\93\93W1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â¬\88*[h, o] W2 →
+                       â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}W1.T1 â¬\88*[h, o] ⓓ{a}W2.ⓐV2.T2.
 #h #o #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H @(cpxs_ind … H) -W2
 /3 width=5 by cpxs_trans, cpxs_theta_dx, cpxs_bind_dx/
 qed.
 
 theorem cpxs_theta: ∀h,o,a,G,L,V1,V,V2,W1,W2,T1,T2.
-                    â¬\86[0, 1] V â\89¡ V2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â\9e¡*[h, o] W2 →
-                    â¦\83G, L.â\93\93W1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V →
-                    â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}W1.T1 â\9e¡*[h, o] ⓓ{a}W2.ⓐV2.T2.
+                    â¬\86[0, 1] V â\89¡ V2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ W1 â¬\88*[h, o] W2 →
+                    â¦\83G, L.â\93\93W1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V →
+                    â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}W1.T1 â¬\88*[h, o] ⓓ{a}W2.ⓐV2.T2.
 #h #o #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1
 /3 width=5 by cpxs_trans, cpxs_theta_rc, cpxs_flat_dx/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_appl1: â\88\80h,o,G,L,V1,T1,U2. â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.T1 â\9e¡*[h, o] U2 →
-                      â\88¨â\88¨ â\88\83â\88\83V2,T2.       â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V2 & â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 &
+lemma cpxs_inv_appl1: â\88\80h,o,G,L,V1,T1,U2. â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.T1 â¬\88*[h, o] U2 →
+                      â\88¨â\88¨ â\88\83â\88\83V2,T2.       â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V2 & â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] T2 &
                                         U2 = ⓐV2. T2
-                       | â\88\83â\88\83a,W,T.       â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] â\93\9b{a}W.T & â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}â\93\9dW.V1.T â\9e¡*[h, o] U2
-                       | â\88\83â\88\83a,V0,V2,V,T. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡*[h, o] V0 & ⬆[0,1] V0 ≡ V2 &
-                                        â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] â\93\93{a}V.T & â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}V.â\93\90V2.T â\9e¡*[h, o] U2.
+                       | â\88\83â\88\83a,W,T.       â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] â\93\9b{a}W.T & â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}â\93\9dW.V1.T â¬\88*[h, o] U2
+                       | â\88\83â\88\83a,V0,V2,V,T. â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88*[h, o] V0 & ⬆[0,1] V0 ≡ V2 &
+                                        â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] â\93\93{a}V.T & â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}V.â\93\90V2.T â¬\88*[h, o] U2.
 #h #o #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5 by or3_intro0, ex3_2_intro/ ]
 #U #U2 #_ #HU2 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct
@@ -108,9 +108,9 @@ lemma lpx_cpx_trans: ∀h,o,G. b_c_transitive … (cpx h o G) (λ_.lpx h o G).
 ]
 qed-.
 
-lemma cpx_bind2: â\88\80h,o,G,L,V1,V2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, o] V2 →
-                 â\88\80I,T1,T2. â¦\83G, L.â\93\91{I}V2â¦\84 â\8a¢ T1 â\9e¡[h, o] T2 →
-                 â\88\80a. â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â\9e¡*[h, o] ⓑ{a,I}V2.T2.
+lemma cpx_bind2: â\88\80h,o,G,L,V1,V2. â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h, o] V2 →
+                 â\88\80I,T1,T2. â¦\83G, L.â\93\91{I}V2â¦\84 â\8a¢ T1 â¬\88[h, o] T2 →
+                 â\88\80a. â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â¬\88*[h, o] ⓑ{a,I}V2.T2.
 /4 width=5 by lpx_cpx_trans, cpxs_bind_dx, lpx_pair/ qed.
 
 (* Advanced properties ******************************************************)
@@ -119,16 +119,16 @@ lemma lpx_cpxs_trans: ∀h,o,G. b_rs_transitive … (cpx h o G) (λ_.lpx h o G).
 #h #o #G @b_c_trans_LTC1 /2 width=3 by lpx_cpx_trans/ (**) (* full auto fails *)
 qed-.
 
-lemma cpxs_bind2_dx: â\88\80h,o,G,L,V1,V2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, o] V2 →
-                     â\88\80I,T1,T2. â¦\83G, L.â\93\91{I}V2â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
-                     â\88\80a. â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â\9e¡*[h, o] ⓑ{a,I}V2.T2.
+lemma cpxs_bind2_dx: â\88\80h,o,G,L,V1,V2. â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h, o] V2 →
+                     â\88\80I,T1,T2. â¦\83G, L.â\93\91{I}V2â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
+                     â\88\80a. â¦\83G, Lâ¦\84 â\8a¢ â\93\91{a,I}V1.T1 â¬\88*[h, o] ⓑ{a,I}V2.T2.
 /4 width=5 by lpx_cpxs_trans, cpxs_bind_dx, lpx_pair/ qed.
 
 (* Properties on supclosure *************************************************)
 
 lemma fqu_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
+                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 → (T2 = U2 → ⊥) →
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1)
   #U2 #HVU2 @(ex3_intro … U2)
@@ -156,8 +156,8 @@ lemma fqu_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2,
 qed-.
 
 lemma fquq_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 → (T2 = U2 → ⊥) →
-                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 → (T2 = U2 → ⊥) →
+                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fquq_inv_gen … H12) -H12
 [ #H12 elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -166,8 +166,8 @@ lemma fquq_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃
 qed-.
 
 lemma fqup_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 → (T2 = U2 → ⊥) →
-                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
+                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 → (T2 = U2 → ⊥) →
+                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -178,8 +178,8 @@ lemma fqup_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2
 qed-.
 
 lemma fqus_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 → (T2 = U2 → ⊥) →
-                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+                           â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 → (T2 = U2 → ⊥) →
+                           â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_gen … H12) -H12
 [ #H12 elim (fqup_cpxs_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/