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[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 4740fc09278589f7bb42052736016135b9f20d5e..60ddf6394ca9621351724650c5f18c663e286940 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/rt_computation/cpxs.ma".
 theorem cpxs_trans: ∀h,G,L. Transitive … (cpxs h G L).
 normalize /2 width=3 by trans_TC/ qed-.
 
-theorem cpxs_bind: ∀h,p,I,G,L,V1,V2,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬈*[h] T2 →
-                   ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+theorem cpxs_bind: ∀h,p,I,G,L,V1,V2,T1,T2. ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬈*[h] T2 →
+                   ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
+                   ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
 #h #p #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: ∀h,I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
-                   ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬈*[h] ⓕ{I}V2.T2.
+theorem cpxs_flat: ∀h,I,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
+                   ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
+                   ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ⬈*[h] ⓕ{I}V2.T2.
 #h #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,p,G,L,V1,V2,W1,W2,T1,T2.
-                      ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ W1 ⬈*[h] W2 →
-                      ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
+                      ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
+                      ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
 #h #p #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,p,G,L,V1,V2,W1,W2,T1,T2.
-                   ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ W1 ⬈*[h] W2 → ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
+                   ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 → ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
+                   ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
 #h #p #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,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                       ⦃G, L⦄ ⊢ V1 ⬈[h] V → ⬆*[1] V ≘ V2 →
-                       ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ W1 ⬈*[h] W2 →
-                       ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
+                       ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⬆*[1] V ≘ V2 →
+                       ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
+                       ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
 #h #p #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,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                    ⬆*[1] V ≘ V2 → ⦃G, L⦄ ⊢ W1 ⬈*[h] W2 →
-                    ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L⦄ ⊢ V1 ⬈*[h] V →
-                    ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
+                    ⬆*[1] V ≘ V2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
+                    ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ V1 ⬈*[h] V →
+                    ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
 #h #p #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: ∀h,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ⬈*[h] U2 →
-                      ∨∨ ∃∃V2,T2.       ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 &
+lemma cpxs_inv_appl1: ∀h,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓐV1.T1 ⬈*[h] U2 →
+                      ∨∨ ∃∃V2,T2.       ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 &
                                         U2 = ⓐV2.T2
-                       | ∃∃p,W,T.       ⦃G, L⦄ ⊢ T1 ⬈*[h] ⓛ{p}W.T & ⦃G, L⦄ ⊢ ⓓ{p}ⓝW.V1.T ⬈*[h] U2
-                       | ∃∃p,V0,V2,V,T. ⦃G, L⦄ ⊢ V1 ⬈*[h] V0 & ⬆*[1] V0 ≘ V2 &
-                                        ⦃G, L⦄ ⊢ T1 ⬈*[h] ⓓ{p}V.T & ⦃G, L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] U2.
+                       | ∃∃p,W,T.       ⦃G,L⦄ ⊢ T1 ⬈*[h] ⓛ{p}W.T & ⦃G,L⦄ ⊢ ⓓ{p}ⓝW.V1.T ⬈*[h] U2
+                       | ∃∃p,V0,V2,V,T. ⦃G,L⦄ ⊢ V1 ⬈*[h] V0 & ⬆*[1] V0 ≘ V2 &
+                                        ⦃G,L⦄ ⊢ T1 ⬈*[h] ⓓ{p}V.T & ⦃G,L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] U2.
 #h #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