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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
index 276a8a03abb1818af4dc8c19e74165c800261c92..35a28700a457df918cbf976fd339b724f9075bbb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cir.ma
@@ -24,35 +24,35 @@ interpretation "context-sensitive irreducibility (term)"
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cir_inv_delta: ∀G,L,K,V,i. ⇩[0, i] L ≡ K.ⓓV → ⦃G, L⦄ ⊢ 𝐈⦃#i⦄ → ⊥.
-/3 width=3/ qed-.
+lemma cir_inv_delta: ∀G,L,K,V,i. ⇩[i] L ≡ K.ⓓV → ⦃G, L⦄ ⊢ 𝐈⦃#i⦄ → ⊥.
+/3 width=3 by crr_delta/ qed-.
 
 lemma cir_inv_ri2: ∀I,G,L,V,T. ri2 I → ⦃G, L⦄ ⊢ 𝐈⦃②{I}V.T⦄ → ⊥.
-/3 width=1/ qed-.
+/3 width=1 by crr_ri2/ qed-.
 
 lemma cir_inv_ib2: ∀a,I,G,L,V,T. ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
                    ⦃G, L⦄ ⊢ 𝐈⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄.
-/4 width=1/ qed-.
+/4 width=1 by crr_ib2_sn, crr_ib2_dx, conj/ qed-.
 
 lemma cir_inv_bind: ∀a,I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄ & ib2 a I.
 #a * [ elim a -a ]
-#G #L #V #T #H [ elim H -H /3 width=1/ ]
-elim (cir_inv_ib2 … H) -H /2 width=1/ /3 width=1/
+#G #L #V #T #H [ elim H -H /3 width=1 by crr_ri2, or_introl/ ]
+elim (cir_inv_ib2 … H) -H /3 width=1 by and3_intro, or_introl/
 qed-.
 
 lemma cir_inv_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄.
 #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 crr_beta, crr_theta/
 qed-.
 
 lemma cir_inv_flat: ∀I,G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃ⓕ{I}V.T⦄ →
                     ∧∧ ⦃G, L⦄ ⊢ 𝐈⦃V⦄ & ⦃G, L⦄ ⊢ 𝐈⦃T⦄ & 𝐒⦃T⦄ & I = Appl.
 * #G #L #V #T #H
-[ elim (cir_inv_appl … H) -H /2 width=1/
-| elim (cir_inv_ri2 … H) -H /2 width=1/
+[ elim (cir_inv_appl … H) -H /2 width=1 by and4_intro/
+| elim (cir_inv_ri2 … H) -H //
 ]
 qed-.
 
@@ -70,10 +70,10 @@ lemma tir_atom: ∀G,I. ⦃G, ⋆⦄ ⊢ 𝐈⦃⓪{I}⦄.
 lemma cir_ib2: ∀a,I,G,L,V,T.
                ib2 a I → ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓑ{a,I}V.T⦄.
 #a #I #G #L #V #T #HI #HV #HT #H
-elim (crr_inv_ib2 … HI H) -HI -H /2 width=1/
+elim (crr_inv_ib2 … HI H) -HI -H /2 width=1 by/
 qed.
 
 lemma cir_appl: ∀G,L,V,T. ⦃G, L⦄ ⊢ 𝐈⦃V⦄ → ⦃G, L⦄ ⊢ 𝐈⦃T⦄ →  𝐒⦃T⦄ → ⦃G, L⦄ ⊢ 𝐈⦃ⓐV.T⦄.
 #G #L #V #T #HV #HT #H1 #H2
-elim (crr_inv_appl … H2) -H2 /2 width=1/
+elim (crr_inv_appl … H2) -H2 /2 width=1 by/
 qed.