X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Frex_drops.ma;h=d7ed815cdbd6ef5e1ed61ba33ec884d06248105b;hb=eba13527cf74de399b7e5b958901962666d4cd25;hp=b6374ac0b04edbdd5bbe445b8c16e038b79282fa;hpb=dc605ae41c39773f55381f241b1ed3db4acf5edd;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma index b6374ac0b..d7ed815cd 100644 --- a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma +++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma @@ -27,24 +27,24 @@ definition f_dedropable_sn: definition f_dropable_sn: predicate (relation3 lenv term term) ≝ λR. - ∀b,f,L1,K1. ⇩*[b,f] L1 ≘ K1 → 𝐔❪f❫ → + ∀b,f,L1,K1. ⇩*[b,f] L1 ≘ K1 → 𝐔❨f❩ → ∀L2,U. L1 ⪤[R,U] L2 → ∀T. ⇧*[f] T ≘ U → ∃∃K2. K1 ⪤[R,T] K2 & ⇩*[b,f] L2 ≘ K2. definition f_dropable_dx: predicate (relation3 lenv term term) ≝ λR. ∀L1,L2,U. L1 ⪤[R,U] L2 → - ∀b,f,K2. ⇩*[b,f] L2 ≘ K2 → 𝐔❪f❫ → ∀T. ⇧*[f] T ≘ U → + ∀b,f,K2. ⇩*[b,f] L2 ≘ K2 → 𝐔❨f❩ → ∀T. ⇧*[f] T ≘ U → ∃∃K1. ⇩*[b,f] L1 ≘ K1 & K1 ⪤[R,T] K2. definition f_transitive_next: relation3 … ≝ λR1,R2,R3. - ∀f,L,T. L ⊢ 𝐅+❪T❫ ≘ f → + ∀f,L,T. L ⊢ 𝐅+❨T❩ ≘ f → ∀g,I,K,i. ⇩[i] L ≘ K.ⓘ[I] → ↑g = ⫰*[i] f → R_pw_transitive_sex (cext2 R1) (cext2 R2) (cext2 R3) (cext2 R1) cfull g K I. definition f_confluent1_next: relation2 … ≝ λR1,R2. - ∀f,L,T. L ⊢ 𝐅+❪T❫ ≘ f → + ∀f,L,T. L ⊢ 𝐅+❨T❩ ≘ f → ∀g,I,K,i. ⇩[i] L ≘ K.ⓘ[I] → ↑g = ⫰*[i] f → R_pw_confluent1_sex (cext2 R1) (cext2 R1) (cext2 R2) cfull g K I. @@ -112,7 +112,7 @@ qed-. (* Basic_2A1: uses: llpx_sn_inv_lift_O *) lemma rex_inv_lifts_bi (R): - ∀L1,L2,U. L1 ⪤[R,U] L2 → ∀b,f. 𝐔❪f❫ → + ∀L1,L2,U. L1 ⪤[R,U] L2 → ∀b,f. 𝐔❨f❩ → ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 → ∀T. ⇧*[f] T ≘ U → K1 ⪤[R,T] K2. #R #L1 #L2 #U #HL12 #b #f #Hf #K1 #K2 #HLK1 #HLK2 #T #HTU @@ -149,7 +149,7 @@ qed-. lemma rex_inv_lref_unit_sn (R): ∀L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K1. ⇩[i] L1 ≘ K1.ⓤ[I] → - ∃∃f,K2. ⇩[i] L2 ≘ K2.ⓤ[I] & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈❪f❫. + ∃∃f,K2. ⇩[i] L2 ≘ K2.ⓤ[I] & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈❨f❩. #R #L1 #L2 #i #HL12 #I #K1 #HLK1 elim (rex_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 // #Y #HY #HLK2 elim (rex_inv_zero_unit_sn … HY) -HY #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/ @@ -157,7 +157,7 @@ qed-. lemma rex_inv_lref_unit_dx (R): ∀L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K2. ⇩[i] L2 ≘ K2.ⓤ[I] → - ∃∃f,K1. ⇩[i] L1 ≘ K1.ⓤ[I] & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈❪f❫. + ∃∃f,K1. ⇩[i] L1 ≘ K1.ⓤ[I] & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈❨f❩. #R #L1 #L2 #i #HL12 #I #K2 #HLK2 elim (rex_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 // #Y #HLK1 #HY elim (rex_inv_zero_unit_dx … HY) -HY #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/