partial commit: "computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_tstc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
index 03566d55696d01e4729b5a0e765ba82726c067c7..062aac6de09340460336c6bab2dc5a732f54696b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
@@ -19,14 +19,14 @@ include "basic_2/computation/lpxs_cpxs.ma".
 
 (* Forward lemmas involving same top term constructor ***********************)
 
-lemma cpxs_fwd_cnx: ∀h,g,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ∀U. ⦃G, L⦄ ⊢ T ➡*[h, g] U → T ≃ U.
-#h #g #L #T #HT #U #H
->(cpxs_inv_cnx1 … H HT) -L -T //
+lemma cpxs_fwd_cnx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ∀U. ⦃G, L⦄ ⊢ T ➡*[h, g] U → T ≃ U.
+#h #g #G #L #T #HT #U #H
+>(cpxs_inv_cnx1 … H HT) -G -L -T //
 qed-.
 
-lemma cpxs_fwd_sort: ∀h,g,L,U,k. ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] U →
+lemma cpxs_fwd_sort: ∀h,g,G,L,U,k. ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] U →
                      ⋆k ≃ U ∨ ⦃G, L⦄ ⊢ ⋆(next h k) ➡*[h, g] U.
-#h #g #L #U #k #H
+#h #g #G #L #U #k #H
 elim (cpxs_inv_sort1 … H) -H #n #l generalize in match k; -k @(nat_ind_plus … n) -n
 [ #k #_ #H -l destruct /2 width=1/
 | #n #IHn #k >plus_plus_comm_23 #Hnl #H destruct
@@ -41,9 +41,9 @@ elim (cpxs_inv_sort1 … H) -H #n #l generalize in match k; -k @(nat_ind_plus 
 qed-.
 
 (* Basic_1: was just: pr3_iso_beta *)
-lemma cpxs_fwd_beta: ∀h,g,a,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{a}W.T ➡*[h, g] U →
+lemma cpxs_fwd_beta: ∀h,g,a,G,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{a}W.T ➡*[h, g] U →
                      ⓐV.ⓛ{a}W.T ≃ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V.T ➡*[h, g] U.
-#h #g #a #L #V #W #T #U #H
+#h #g #a #G #L #V #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1/
 | #b #W0 #T0 #HT0 #HU
@@ -56,21 +56,21 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 (* Note: probably this is an inversion lemma *)
-lemma cpxs_fwd_delta: ∀h,g,I,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
+lemma cpxs_fwd_delta: ∀h,g,I,G,L,K,V1,i. ⇩[0, i] L ≡ K.ⓑ{I}V1 →
                       ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
                       ∀U. ⦃G, L⦄ ⊢ #i ➡*[h, g] U →
                       #i ≃ U ∨ ⦃G, L⦄ ⊢ V2 ➡*[h, g] U.
-#h #g #I #L #K #V1 #i #HLK #V2 #HV12 #U #H
+#h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
 elim (cpxs_inv_lref1 … H) -H /2 width=1/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
 lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK) -HLK /3 width=9/
 qed-.
 
-lemma cpxs_fwd_theta: ∀h,g,a,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}V.T ➡*[h, g] U →
+lemma cpxs_fwd_theta: ∀h,g,a,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}V.T ➡*[h, g] U →
                       ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≃ U ∨
                       ⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡*[h, g] U.
-#h #g #a #L #V1 #V #T #U #H #V2 #HV12
+#h #g #a #G #L #V1 #V #T #U #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1/
 | #b #W #T0 #HT0 #HU
@@ -99,9 +99,9 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_cast: ∀h,g,L,W,T,U. ⦃G, L⦄ ⊢ ⓝW.T ➡*[h, g] U →
+lemma cpxs_fwd_cast: ∀h,g,G,L,W,T,U. ⦃G, L⦄ ⊢ ⓝW.T ➡*[h, g] U →
                      ∨∨ ⓝW. T ≃ U | ⦃G, L⦄ ⊢ T ➡*[h, g] U | ⦃G, L⦄ ⊢ W ➡*[h, g] U.
-#h #g #L #W #T #U #H
+#h #g #G #L #W #T #U #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1/
 qed-.