X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fsubstitution%2Flift_lift.ma;h=6feb72e036f9f8813e46d0eb6b9d561d588c7448;hb=f75be90562ddd964ef7ed43b956eb908f3133e3a;hp=3a5d85355fddf42372a79a1952a59abac0912bd4;hpb=78f21d7d9014e5c7655f58239e4f1a128ea2c558;p=helm.git diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma index 3a5d85355..6feb72e03 100644 --- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma +++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/lift_lift.ma @@ -27,6 +27,8 @@ theorem lift_inj: ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U lapply (lift_inv_lref2_lt … HX ?) -HX // | #i #d #e #Hdi #X #HX lapply (lift_inv_lref2_ge … HX ?) -HX /2/ +| #p #d #e #X #HX + lapply (lift_inv_gref2 … HX) -HX // | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX elim (lift_inv_bind2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX @@ -44,28 +46,30 @@ theorem lift_div_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → lapply (lift_inv_sort2 … Hk) -Hk #Hk destruct -T2 /3/ | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12 lapply (lt_to_le_to_lt … Hid1 Hd12) -Hd12 #Hid2 - lapply (lift_inv_lref2_lt … Hi ?) -Hi /3/ + lapply (lift_inv_lref2_lt … Hi ?) -Hi /2/ /3/ | #i #d1 #e1 #Hid1 #d2 #e2 #T2 #Hi #Hd12 elim (lift_inv_lref2 … Hi) -Hi * #Hid2 #H destruct -T2 [ -Hd12; lapply (lt_plus_to_lt_l … Hid2) -Hid2 #Hid2 /3/ | -Hid1; lapply (arith1 … Hid2) -Hid2 #Hid2 @(ex2_1_intro … #(i - e2)) [ >le_plus_minus_comm [ @lift_lref_ge @(transitive_le … Hd12) -Hd12 /2/ | -Hd12 /2/ ] - | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %) /3/ + | -Hd12 >(plus_minus_m_m i e2) in ⊢ (? ? ? ? %) /2/ /3/ ] ] +| #p #d1 #e1 #d2 #e2 #T2 #Hk #Hd12 + lapply (lift_inv_gref2 … Hk) -Hk #Hk destruct -T2 /3/ | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 lapply (lift_inv_bind2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2; elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1 - >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /3 width = 5/ + >plus_plus_comm_23 in HU2 #HU2 elim (IHU … HU2 ?) /2/ /3 width = 5/ | #I #W1 #W #U1 #U #d1 #e1 #_ #_ #IHW #IHU #d2 #e2 #T2 #H #Hd12 lapply (lift_inv_flat2 … H) -H * #W2 #U2 #HW2 #HU2 #H destruct -T2; elim (IHW … HW2 ?) // -IHW HW2 #W0 #HW2 #HW1 - elim (IHU … HU2 ?) /3 width = 5/ + elim (IHU … HU2 ?) // /3 width = 5/ ] qed. -theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 → U1 = U2. +theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 → U1 = U2. #d #e #T #U1 #H elim H -H d e T U1 [ #k #d #e #X #HX lapply (lift_inv_sort1 … HX) -HX // @@ -73,6 +77,8 @@ theorem lift_mono: ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 lapply (lift_inv_lref1_lt … HX ?) -HX // | #i #d #e #Hdi #X #HX lapply (lift_inv_lref1_ge … HX ?) -HX // +| #p #d #e #X #HX + lapply (lift_inv_gref1 … HX) -HX // | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX elim (lift_inv_bind1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/ | #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX @@ -95,6 +101,8 @@ theorem lift_trans_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → [ @(transitive_le … Hd21 ?) -Hd21 /2/ | -Hd21 /2/ ] +| #p #d1 #e1 #d2 #e2 #T2 #HT2 #_ #_ + >(lift_inv_gref1 … HT2) -HT2 // | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21 elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10 @@ -102,7 +110,7 @@ theorem lift_trans_be: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd12 #Hd21 elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; lapply (IHV12 … HV20 ? ?) // -IHV12 HV20 #HV10 - lapply (IHT12 … HT20 ? ?) /2/ + lapply (IHT12 … HT20 ? ?) // /2/ ] qed. @@ -115,19 +123,21 @@ theorem lift_trans_le: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → >(lift_inv_sort1 … HX) -HX /2/ | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_ lapply (lt_to_le_to_lt … (d1+e2) Hid1 ?) // #Hie2 - elim (lift_inv_lref1 … HX) -HX * #Hid2 #HX destruct -X /4/ + elim (lift_inv_lref1 … HX) -HX * #Hid2 #HX destruct -X /3/ /4/ | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #Hd21 lapply (transitive_le … Hd21 Hid1) -Hd21 #Hid2 lapply (lift_inv_lref1_ge … HX ?) -HX /2/ #HX destruct -X; >plus_plus_comm_23 /4/ +| #p #d1 #e1 #d2 #e2 #X #HX #_ + >(lift_inv_gref1 … HX) -HX /2/ | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; elim (IHV12 … HV20 ?) -IHV12 HV20 // - elim (IHT12 … HT20 ?) -IHT12 HT20 /3 width=5/ + elim (IHT12 … HT20 ?) -IHT12 HT20 /2/ /3 width=5/ | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hd21 elim (lift_inv_flat1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; elim (IHV12 … HV20 ?) -IHV12 HV20 // - elim (IHT12 … HT20 ?) -IHT12 HT20 /3 width=5/ + elim (IHT12 … HT20 ?) -IHT12 HT20 // /3 width=5/ ] qed. @@ -145,15 +155,17 @@ theorem lift_trans_ge: ∀d1,e1,T1,T. ↑[d1, e1] T1 ≡ T → lapply (lift_inv_lref1_lt … HX ?) -HX // #HX destruct -X /3/ | #i #d1 #e1 #Hid1 #d2 #e2 #X #HX #_ elim (lift_inv_lref1 … HX) -HX * #Hied #HX destruct -X; - [2: >plus_plus_comm_23] /4/ + [ /4/ | >plus_plus_comm_23 /4/ ] +| #p #d1 #e1 #d2 #e2 #X #HX #_ + >(lift_inv_gref1 … HX) -HX /2/ | #I #V1 #V2 #T1 #T2 #d1 #e1 #_ #_ #IHV12 #IHT12 #d2 #e2 #X #HX #Hded elim (lift_inv_bind1 … HX) -HX #V0 #T0 #HV20 #HT20 #HX destruct -X; elim (IHV12 … HV20 ?) -IHV12 HV20 // elim (IHT12 … HT20 ?) -IHT12 HT20 /2/ #T -