X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpms_drops.ma;h=12f11ae451db36acbcd54b93bb348e6427062c79;hb=f308429a0fde273605a2330efc63268b4ac36c99;hp=e05d49b0bd0d15eeb0a08540abbdaa3c9c1ffeef;hpb=ede00573e3e4cb28df7ca9a5dae6228c2b432608;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma index e05d49b0b..12f11ae45 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma @@ -46,8 +46,8 @@ qed-. (* Advanced properties ******************************************************) -lemma cpms_delta (n) (h) (G): ∀K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡*[n, h] V2 → - ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G, K.ⓓV1⦄ ⊢ #0 ➡*[n, h] W2. +lemma cpms_delta (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 → + ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G,K.ⓓV1⦄ ⊢ #0 ➡*[n,h] W2. #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2 [ /3 width=3 by cpm_cpms, cpm_delta/ | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2 @@ -56,8 +56,8 @@ lemma cpms_delta (n) (h) (G): ∀K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡*[n, h] V2 → ] qed. -lemma cpms_ell (n) (h) (G): ∀K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡*[n, h] V2 → - ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G, K.ⓛV1⦄ ⊢ #0 ➡*[↑n, h] W2. +lemma cpms_ell (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 → + ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G,K.ⓛV1⦄ ⊢ #0 ➡*[↑n,h] W2. #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2 [ /3 width=3 by cpm_cpms, cpm_ell/ | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2 @@ -66,8 +66,8 @@ lemma cpms_ell (n) (h) (G): ∀K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡*[n, h] V2 → ] qed. -lemma cpms_lref (n) (h) (I) (G): ∀K,T,i. ⦃G, K⦄ ⊢ #i ➡*[n, h] T → - ∀U. ⬆*[1] T ≘ U → ⦃G, K.ⓘ{I}⦄ ⊢ #↑i ➡*[n, h] U. +lemma cpms_lref (n) (h) (I) (G): ∀K,T,i. ⦃G,K⦄ ⊢ #i ➡*[n,h] T → + ∀U. ⬆*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ➡*[n,h] U. #n #h #I #G #K #T #i #H @(cpms_ind_dx … H) -T [ /3 width=3 by cpm_cpms, cpm_lref/ | #n1 #n2 #T #T2 #_ #IH #HT2 #U2 #HTU2 @@ -77,9 +77,9 @@ lemma cpms_lref (n) (h) (I) (G): ∀K,T,i. ⦃G, K⦄ ⊢ #i ➡*[n, h] T → qed. lemma cpms_cast_sn (n) (h) (G) (L): - ∀U1,U2. ⦃G, L⦄ ⊢ U1 ➡*[n, h] U2 → - ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → - ⦃G, L⦄ ⊢ ⓝU1.T1 ➡*[n, h] ⓝU2.T2. + ∀U1,U2. ⦃G,L⦄ ⊢ U1 ➡*[n,h] U2 → + ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → + ⦃G,L⦄ ⊢ ⓝU1.T1 ➡*[n,h] ⓝU2.T2. #n #h #G #L #U1 #U2 #H @(cpms_ind_sn … H) -U1 -n [ /3 width=3 by cpm_cpms, cpm_cast/ | #n1 #n2 #U1 #U #HU1 #_ #IH #T1 #T2 #H @@ -92,8 +92,8 @@ qed. (* Basic_2A1: uses: cprs_delta *) lemma cpms_delta_drops (n) (h) (G): ∀L,K,V,i. ⬇*[i] L ≘ K.ⓓV → - ∀V2. ⦃G, K⦄ ⊢ V ➡*[n, h] V2 → - ∀W2. ⬆*[↑i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ➡*[n, h] W2. + ∀V2. ⦃G,K⦄ ⊢ V ➡*[n,h] V2 → + ∀W2. ⬆*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ➡*[n,h] W2. #n #h #G #L #K #V #i #HLK #V2 #H @(cpms_ind_dx … H) -V2 [ /3 width=6 by cpm_cpms, cpm_delta_drops/ | #n1 #n2 #V1 #V2 #_ #IH #HV12 #W2 #HVW2 @@ -105,8 +105,8 @@ qed. lemma cpms_ell_drops (n) (h) (G): ∀L,K,W,i. ⬇*[i] L ≘ K.ⓛW → - ∀W2. ⦃G, K⦄ ⊢ W ➡*[n, h] W2 → - ∀V2. ⬆*[↑i] W2 ≘ V2 → ⦃G, L⦄ ⊢ #i ➡*[↑n, h] V2. + ∀W2. ⦃G,K⦄ ⊢ W ➡*[n,h] W2 → + ∀V2. ⬆*[↑i] W2 ≘ V2 → ⦃G,L⦄ ⊢ #i ➡*[↑n,h] V2. #n #h #G #L #K #W #i #HLK #W2 #H @(cpms_ind_dx … H) -W2 [ /3 width=6 by cpm_cpms, cpm_ell_drops/ | #n1 #n2 #W1 #W2 #_ #IH #HW12 #V2 #HWV2 @@ -119,11 +119,11 @@ qed. (* Advanced inversion lemmas ************************************************) lemma cpms_inv_lref1_drops (n) (h) (G): - ∀L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[n, h] T2 → + ∀L,T2,i. ⦃G,L⦄ ⊢ #i ➡*[n,h] T2 → ∨∨ ∧∧ T2 = #i & n = 0 - | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ➡*[n, h] V2 & + | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ➡*[n,h] V2 & ⬆*[↑i] V2 ≘ T2 - | ∃∃m,K,V,V2. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ➡*[m, h] V2 & + | ∃∃m,K,V,V2. ⬇*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ➡*[m,h] V2 & ⬆*[↑i] V2 ≘ T2 & n = ↑m. #n #h #G #L #T2 #i #H @(cpms_ind_dx … H) -T2 [ /3 width=1 by or3_intro0, conj/ @@ -146,9 +146,59 @@ lemma cpms_inv_lref1_drops (n) (h) (G): ] qed-. +lemma cpms_inv_delta_sn (n) (h) (G) (K) (V): + ∀T2. ⦃G,K.ⓓV⦄ ⊢ #0 ➡*[n,h] T2 → + ∨∨ ∧∧ T2 = #0 & n = 0 + | ∃∃V2. ⦃G,K⦄ ⊢ V ➡*[n,h] V2 & ⬆*[1] V2 ≘ T2. +#n #h #G #K #V #T2 #H +elim (cpms_inv_lref1_drops … H) -H * +[ /3 width=1 by or_introl, conj/ +| #Y #X #V2 #H #HV2 #HVT2 + lapply (drops_fwd_isid … H ?) -H [ // ] #H destruct + /3 width=3 by ex2_intro, or_intror/ +| #m #Y #X #V2 #H #HV2 #HVT2 + lapply (drops_fwd_isid … H ?) -H [ // ] #H destruct +] +qed-. + +lemma cpms_inv_ell_sn (n) (h) (G) (K) (V): + ∀T2. ⦃G,K.ⓛV⦄ ⊢ #0 ➡*[n,h] T2 → + ∨∨ ∧∧ T2 = #0 & n = 0 + | ∃∃m,V2. ⦃G,K⦄ ⊢ V ➡*[m,h] V2 & ⬆*[1] V2 ≘ T2 & n = ↑m. +#n #h #G #K #V #T2 #H +elim (cpms_inv_lref1_drops … H) -H * +[ /3 width=1 by or_introl, conj/ +| #Y #X #V2 #H #HV2 #HVT2 + lapply (drops_fwd_isid … H ?) -H [ // ] #H destruct +| #m #Y #X #V2 #H #HV2 #HVT2 #H0 destruct + lapply (drops_fwd_isid … H ?) -H [ // ] #H destruct + /3 width=5 by ex3_2_intro, or_intror/ +] +qed-. + +lemma cpms_inv_lref_sn (n) (h) (G) (I) (K): + ∀U2,i. ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ➡*[n,h] U2 → + ∨∨ ∧∧ U2 = #↑i & n = 0 + | ∃∃T2. ⦃G,K⦄ ⊢ #i ➡*[n,h] T2 & ⬆*[1] T2 ≘ U2. +#n #h #G #I #K #U2 #i #H +elim (cpms_inv_lref1_drops … H) -H * +[ /3 width=1 by or_introl, conj/ +| #L #V #V2 #H #HV2 #HVU2 + lapply (drops_inv_drop1 … H) -H #HLK + elim (lifts_split_trans … HVU2 (𝐔❴↑i❵) (𝐔❴1❵)) -HVU2 + [| // ] #T2 #HVT2 #HTU2 + /4 width=6 by cpms_delta_drops, ex2_intro, or_intror/ +| #m #L #V #V2 #H #HV2 #HVU2 #H0 destruct + lapply (drops_inv_drop1 … H) -H #HLK + elim (lifts_split_trans … HVU2 (𝐔❴↑i❵) (𝐔❴1❵)) -HVU2 + [| // ] #T2 #HVT2 #HTU2 + /4 width=6 by cpms_ell_drops, ex2_intro, or_intror/ +] +qed-. + fact cpms_inv_succ_sn (n) (h) (G) (L): - ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[↑n, h] T2 → - ∃∃T. ⦃G, L⦄ ⊢ T1 ➡*[1, h] T & ⦃G, L⦄ ⊢ T ➡*[n, h] T2. + ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[↑n,h] T2 → + ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[1,h] T & ⦃G,L⦄ ⊢ T ➡*[n,h] T2. #n #h #G #L #T1 #T2 @(insert_eq_0 … (↑n)) #m #H @(cpms_ind_sn … H) -T1 -m