some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/aaa.ma b/matita/matita/contribs/lambdadelta/static_2/static/aaa.ma
index b7e9ca046cdf55052a7eb343a3fff47efb779ae2..d204bdc21a729689a9def69e6cf0bed133f60300 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/aaa.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/aaa.ma
@@ -37,7 +37,7 @@ interpretation "atomic arity assignment (term)"
 
 (* Basic inversion lemmas ***************************************************)
 
-fact aaa_inv_sort_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀s. T = ⋆s → A = ⓪.
+fact aaa_inv_sort_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀s. T = ⋆s → A = ⓪.
 #G #L #T #A * -G -L -T -A //
 [ #I #G #L #V #B #_ #s #H destruct
 | #I #G #L #A #i #_ #s #H destruct
@@ -48,11 +48,11 @@ fact aaa_inv_sort_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀s. T = ⋆s →
 ]
 qed-.
 
-lemma aaa_inv_sort: ∀G,L,A,s. ⦃G, L⦄ ⊢ ⋆s ⁝ A → A = ⓪.
+lemma aaa_inv_sort: ∀G,L,A,s. ⦃G,L⦄ ⊢ ⋆s ⁝ A → A = ⓪.
 /2 width=6 by aaa_inv_sort_aux/ qed-.
 
-fact aaa_inv_zero_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → T = #0 →
-                       ∃∃I,K,V. L = K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A.
+fact aaa_inv_zero_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → T = #0 →
+                       ∃∃I,K,V. L = K.ⓑ{I}V & ⦃G,K⦄ ⊢ V ⁝ A.
 #G #L #T #A * -G -L -T -A /2 width=5 by ex2_3_intro/
 [ #G #L #s #H destruct
 | #I #G #L #A #i #_ #H destruct
@@ -63,12 +63,12 @@ fact aaa_inv_zero_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → T = #0 →
 ]
 qed-.
 
-lemma aaa_inv_zero: ∀G,L,A. ⦃G, L⦄ ⊢ #0 ⁝ A →
-                    ∃∃I,K,V. L = K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ⁝ A.
+lemma aaa_inv_zero: ∀G,L,A. ⦃G,L⦄ ⊢ #0 ⁝ A →
+                    ∃∃I,K,V. L = K.ⓑ{I}V & ⦃G,K⦄ ⊢ V ⁝ A.
 /2 width=3 by aaa_inv_zero_aux/ qed-.
 
-fact aaa_inv_lref_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀i. T = #(↑i) →
-                       ∃∃I,K. L = K.ⓘ{I} & ⦃G, K⦄ ⊢ #i ⁝ A.
+fact aaa_inv_lref_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀i. T = #(↑i) →
+                       ∃∃I,K. L = K.ⓘ{I} & ⦃G,K⦄ ⊢ #i ⁝ A.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #j #H destruct
 | #I #G #L #V #B #_ #j #H destruct
@@ -80,11 +80,11 @@ fact aaa_inv_lref_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀i. T = #(↑i)
 ]
 qed-.
 
-lemma aaa_inv_lref: ∀G,L,A,i. ⦃G, L⦄ ⊢ #↑i ⁝ A →
-                    ∃∃I,K. L = K.ⓘ{I} & ⦃G, K⦄ ⊢ #i ⁝ A.
+lemma aaa_inv_lref: ∀G,L,A,i. ⦃G,L⦄ ⊢ #↑i ⁝ A →
+                    ∃∃I,K. L = K.ⓘ{I} & ⦃G,K⦄ ⊢ #i ⁝ A.
 /2 width=3 by aaa_inv_lref_aux/ qed-.
 
-fact aaa_inv_gref_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀l. T = §l → ⊥.
+fact aaa_inv_gref_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀l. T = §l → ⊥.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #k #H destruct
 | #I #G #L #V #B #_ #k #H destruct
@@ -96,11 +96,11 @@ fact aaa_inv_gref_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀l. T = §l →
 ]
 qed-.
 
-lemma aaa_inv_gref: ∀G,L,A,l. ⦃G, L⦄ ⊢ §l ⁝ A → ⊥.
+lemma aaa_inv_gref: ∀G,L,A,l. ⦃G,L⦄ ⊢ §l ⁝ A → ⊥.
 /2 width=7 by aaa_inv_gref_aux/ qed-.
 
-fact aaa_inv_abbr_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓓ{p}W.U →
-                       ∃∃B. ⦃G, L⦄ ⊢ W ⁝ B & ⦃G, L.ⓓW⦄ ⊢ U ⁝ A.
+fact aaa_inv_abbr_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓓ{p}W.U →
+                       ∃∃B. ⦃G,L⦄ ⊢ W ⁝ B & ⦃G,L.ⓓW⦄ ⊢ U ⁝ A.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #q #W #U #H destruct
 | #I #G #L #V #B #_ #q #W #U #H destruct
@@ -112,12 +112,12 @@ fact aaa_inv_abbr_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓓ{
 ]
 qed-.
 
-lemma aaa_inv_abbr: ∀p,G,L,V,T,A. ⦃G, L⦄ ⊢ ⓓ{p}V.T ⁝ A →
-                    ∃∃B. ⦃G, L⦄ ⊢ V ⁝ B & ⦃G, L.ⓓV⦄ ⊢ T ⁝ A.
+lemma aaa_inv_abbr: ∀p,G,L,V,T,A. ⦃G,L⦄ ⊢ ⓓ{p}V.T ⁝ A →
+                    ∃∃B. ⦃G,L⦄ ⊢ V ⁝ B & ⦃G,L.ⓓV⦄ ⊢ T ⁝ A.
 /2 width=4 by aaa_inv_abbr_aux/ qed-.
 
-fact aaa_inv_abst_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓛ{p}W.U →
-                       ∃∃B1,B2. ⦃G, L⦄ ⊢ W ⁝ B1 & ⦃G, L.ⓛW⦄ ⊢ U ⁝ B2 & A = ②B1.B2.
+fact aaa_inv_abst_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓛ{p}W.U →
+                       ∃∃B1,B2. ⦃G,L⦄ ⊢ W ⁝ B1 & ⦃G,L.ⓛW⦄ ⊢ U ⁝ B2 & A = ②B1.B2.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #q #W #U #H destruct
 | #I #G #L #V #B #_ #q #W #U #H destruct
@@ -129,12 +129,12 @@ fact aaa_inv_abst_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀p,W,U. T = ⓛ{
 ]
 qed-.
 
-lemma aaa_inv_abst: ∀p,G,L,W,T,A. ⦃G, L⦄ ⊢ ⓛ{p}W.T ⁝ A →
-                    ∃∃B1,B2. ⦃G, L⦄ ⊢ W ⁝ B1 & ⦃G, L.ⓛW⦄ ⊢ T ⁝ B2 & A = ②B1.B2.
+lemma aaa_inv_abst: ∀p,G,L,W,T,A. ⦃G,L⦄ ⊢ ⓛ{p}W.T ⁝ A →
+                    ∃∃B1,B2. ⦃G,L⦄ ⊢ W ⁝ B1 & ⦃G,L.ⓛW⦄ ⊢ T ⁝ B2 & A = ②B1.B2.
 /2 width=4 by aaa_inv_abst_aux/ qed-.
 
-fact aaa_inv_appl_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓐW.U →
-                       ∃∃B. ⦃G, L⦄ ⊢ W ⁝ B & ⦃G, L⦄ ⊢ U ⁝ ②B.A.
+fact aaa_inv_appl_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓐW.U →
+                       ∃∃B. ⦃G,L⦄ ⊢ W ⁝ B & ⦃G,L⦄ ⊢ U ⁝ ②B.A.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #W #U #H destruct
 | #I #G #L #V #B #_ #W #U #H destruct
@@ -146,12 +146,12 @@ fact aaa_inv_appl_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓐW.U
 ]
 qed-.
 
-lemma aaa_inv_appl: ∀G,L,V,T,A. ⦃G, L⦄ ⊢ ⓐV.T ⁝ A →
-                    ∃∃B. ⦃G, L⦄ ⊢ V ⁝ B & ⦃G, L⦄ ⊢ T ⁝ ②B.A.
+lemma aaa_inv_appl: ∀G,L,V,T,A. ⦃G,L⦄ ⊢ ⓐV.T ⁝ A →
+                    ∃∃B. ⦃G,L⦄ ⊢ V ⁝ B & ⦃G,L⦄ ⊢ T ⁝ ②B.A.
 /2 width=3 by aaa_inv_appl_aux/ qed-.
 
-fact aaa_inv_cast_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓝW.U →
-                       ⦃G, L⦄ ⊢ W ⁝ A ∧ ⦃G, L⦄ ⊢ U ⁝ A.
+fact aaa_inv_cast_aux: ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓝW.U →
+                       ⦃G,L⦄ ⊢ W ⁝ A ∧ ⦃G,L⦄ ⊢ U ⁝ A.
 #G #L #T #A * -G -L -T -A
 [ #G #L #s #W #U #H destruct
 | #I #G #L #V #B #_ #W #U #H destruct
@@ -163,6 +163,6 @@ fact aaa_inv_cast_aux: ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀W,U. T = ⓝW.U
 ]
 qed-.
 
-lemma aaa_inv_cast: ∀G,L,W,T,A. ⦃G, L⦄ ⊢ ⓝW.T ⁝ A →
-                    ⦃G, L⦄ ⊢ W ⁝ A ∧ ⦃G, L⦄ ⊢ T ⁝ A.
+lemma aaa_inv_cast: ∀G,L,W,T,A. ⦃G,L⦄ ⊢ ⓝW.T ⁝ A →
+                    ⦃G,L⦄ ⊢ W ⁝ A ∧ ⦃G,L⦄ ⊢ T ⁝ A.
 /2 width=3 by aaa_inv_cast_aux/ qed-.