- commit of the "reduction" component with two additions ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cix.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cix.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cix.ma
index fc1de0d4cf05fef518c0705ec1327ae365a04ca1..d7da41971f5237fceaa8491f7c753d0d5244a50a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cix.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cix.ma
@@ -27,44 +27,44 @@ interpretation "context-sensitive extended irreducibility (term)"
 (* Basic inversion lemmas ***************************************************)
 
 lemma cix_inv_sort: ∀h,g,G,L,k,l. deg h g k (l+1) → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃⋆k⦄ → ⊥.
-/3 width=2/ qed-.
+/3 width=2 by crx_sort/ qed-.
 
-lemma cix_inv_delta: ∀h,g,I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃#i⦄ → ⊥.
-/3 width=4/ qed-.
+lemma cix_inv_delta: ∀h,g,I,G,L,K,V,i. ⇩[i] L ≡ K.ⓑ{I}V → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃#i⦄ → ⊥.
+/3 width=4 by crx_delta/ qed-.
 
 lemma cix_inv_ri2: ∀h,g,I,G,L,V,T. ri2 I → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃②{I}V.T⦄ → ⊥.
-/3 width=1/ qed-.
+/3 width=1 by crx_ri2/ qed-.
 
 lemma cix_inv_ib2: ∀h,g,a,I,G,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓑ{a,I}V.T⦄ →
                    ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈[h, g]⦃T⦄.
-/4 width=1/ qed-.
+/4 width=1 by crx_ib2_sn, crx_ib2_dx, conj/ qed-.
 
 lemma cix_inv_bind: ∀h,g,a,I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓑ{a,I}V.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ & ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈[h, g]⦃T⦄ & ib2 a I.
 #h #g #a * [ elim a -a ]
-#G #L #V #T #H [ elim H -H /3 width=1/ ]
-elim (cix_inv_ib2 … H) -H /2 width=1/ /3 width=1/
+#G #L #V #T #H [ elim H -H /3 width=1 by crx_ri2, or_introl/ ]
+elim (cix_inv_ib2 … H) -H /3 width=1 by and3_intro, or_introl/
 qed-.
 
 lemma cix_inv_appl: ∀h,g,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓐV.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈[h, g]⦃T⦄ & 𝐒⦃T⦄.
 #h #g #G #L #V #T #HVT @and3_intro /3 width=1/
 generalize in match HVT; -HVT elim T -T //
-* // #a * #U #T #_ #_ #H elim H -H /2 width=1/
+* // #a * #U #T #_ #_ #H elim H -H /2 width=1 by crx_beta, crx_theta/
 qed-.
 
 lemma cix_inv_flat: ∀h,g,I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓕ{I}V.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈[h, g]⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
 #h #g * #G #L #V #T #H
-[ elim (cix_inv_appl … H) -H /2 width=1/
-| elim (cix_inv_ri2 … H) -H /2 width=1/
+[ elim (cix_inv_appl … H) -H /2 width=1 by and4_intro/
+| elim (cix_inv_ri2 … H) -H //
 ]
 qed-.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma cix_inv_cir: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ 𝐈[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃T⦄.
-/3 width=1/ qed-.
+/3 width=1 by crr_crx/ qed-.
 
 (* Basic properties *********************************************************)
 
@@ -84,10 +84,10 @@ qed.
 lemma cix_ib2: ∀h,g,a,I,G,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈[h, g]⦃T⦄ →
                                ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓑ{a,I}V.T⦄.
 #h #g #a #I #G #L #V #T #HI #HV #HT #H
-elim (crx_inv_ib2 … HI H) -HI -H /2 width=1/
+elim (crx_inv_ib2 … HI H) -HI -H /2 width=1 by/
 qed.
 
 lemma cix_appl: ∀h,g,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈[h, g]⦃V⦄ → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃T⦄ →  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈[h, g]⦃ⓐV.T⦄.
 #h #g #G #L #V #T #HV #HT #H1 #H2
-elim (crx_inv_appl … H2) -H2 /2 width=1/
+elim (crx_inv_appl … H2) -H2 /2 width=1 by/
 qed.