X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Flift.ma;h=d6537046caf4051af2f50853896f467d95f232ed;hb=43282d3750af8831c8100c60d75c56fdfb7ff3c9;hp=f8848629202d42750d885d59d179636b93995ace;hpb=6c985e4e2e7846a2b9abd0c84569f21c24e9ce2f;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma index f88486292..d6537046c 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma @@ -38,14 +38,14 @@ interpretation "relocation" 'RLift d e T1 T2 = (lift d e T1 T2). (* Basic inversion lemmas ***************************************************) -fact lift_inv_O2_aux: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → e = 0 → T1 = T2. +fact lift_inv_O2_aux: ∀d,e,T1,T2. ⬆[d, e] T1 ≡ T2 → e = 0 → T1 = T2. #d #e #T1 #T2 #H elim H -d -e -T1 -T2 /3 width=1 by eq_f2/ qed-. -lemma lift_inv_O2: ∀d,T1,T2. ⇧[d, 0] T1 ≡ T2 → T1 = T2. +lemma lift_inv_O2: ∀d,T1,T2. ⬆[d, 0] T1 ≡ T2 → T1 = T2. /2 width=4 by lift_inv_O2_aux/ qed-. -fact lift_inv_sort1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k → T2 = ⋆k. +fact lift_inv_sort1_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k → T2 = ⋆k. #d #e #T1 #T2 * -d -e -T1 -T2 // [ #i #d #e #_ #k #H destruct | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct @@ -53,10 +53,10 @@ fact lift_inv_sort1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k ] qed-. -lemma lift_inv_sort1: ∀d,e,T2,k. ⇧[d,e] ⋆k ≡ T2 → T2 = ⋆k. +lemma lift_inv_sort1: ∀d,e,T2,k. ⬆[d,e] ⋆k ≡ T2 → T2 = ⋆k. /2 width=5 by lift_inv_sort1_aux/ qed-. -fact lift_inv_lref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T1 = #i → +fact lift_inv_lref1_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀i. T1 = #i → (i < d ∧ T2 = #i) ∨ (d ≤ i ∧ T2 = #(i + e)). #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #i #H destruct @@ -68,23 +68,23 @@ fact lift_inv_lref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T1 = #i → ] qed-. -lemma lift_inv_lref1: ∀d,e,T2,i. ⇧[d,e] #i ≡ T2 → +lemma lift_inv_lref1: ∀d,e,T2,i. ⬆[d,e] #i ≡ T2 → (i < d ∧ T2 = #i) ∨ (d ≤ i ∧ T2 = #(i + e)). /2 width=3 by lift_inv_lref1_aux/ qed-. -lemma lift_inv_lref1_lt: ∀d,e,T2,i. ⇧[d,e] #i ≡ T2 → i < d → T2 = #i. +lemma lift_inv_lref1_lt: ∀d,e,T2,i. ⬆[d,e] #i ≡ T2 → i < d → T2 = #i. #d #e #T2 #i #H elim (lift_inv_lref1 … H) -H * // #Hdi #_ #Hid lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd elim (lt_refl_false … Hdd) qed-. -lemma lift_inv_lref1_ge: ∀d,e,T2,i. ⇧[d,e] #i ≡ T2 → d ≤ i → T2 = #(i + e). +lemma lift_inv_lref1_ge: ∀d,e,T2,i. ⬆[d,e] #i ≡ T2 → d ≤ i → T2 = #(i + e). #d #e #T2 #i #H elim (lift_inv_lref1 … H) -H * // #Hid #_ #Hdi lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd elim (lt_refl_false … Hdd) qed-. -fact lift_inv_gref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T1 = §p → T2 = §p. +fact lift_inv_gref1_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀p. T1 = §p → T2 = §p. #d #e #T1 #T2 * -d -e -T1 -T2 // [ #i #d #e #_ #k #H destruct | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct @@ -92,12 +92,12 @@ fact lift_inv_gref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T1 = §p → ] qed-. -lemma lift_inv_gref1: ∀d,e,T2,p. ⇧[d,e] §p ≡ T2 → T2 = §p. +lemma lift_inv_gref1: ∀d,e,T2,p. ⬆[d,e] §p ≡ T2 → T2 = §p. /2 width=5 by lift_inv_gref1_aux/ qed-. -fact lift_inv_bind1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → +fact lift_inv_bind1_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀a,I,V1,U1. T1 = ⓑ{a,I} V1.U1 → - ∃∃V2,U2. ⇧[d,e] V1 ≡ V2 & ⇧[d+1,e] U1 ≡ U2 & + ∃∃V2,U2. ⬆[d,e] V1 ≡ V2 & ⬆[d+1,e] U1 ≡ U2 & T2 = ⓑ{a,I} V2. U2. #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #a #I #V1 #U1 #H destruct @@ -109,14 +109,14 @@ fact lift_inv_bind1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ] qed-. -lemma lift_inv_bind1: ∀d,e,T2,a,I,V1,U1. ⇧[d,e] ⓑ{a,I} V1. U1 ≡ T2 → - ∃∃V2,U2. ⇧[d,e] V1 ≡ V2 & ⇧[d+1,e] U1 ≡ U2 & +lemma lift_inv_bind1: ∀d,e,T2,a,I,V1,U1. ⬆[d,e] ⓑ{a,I} V1. U1 ≡ T2 → + ∃∃V2,U2. ⬆[d,e] V1 ≡ V2 & ⬆[d+1,e] U1 ≡ U2 & T2 = ⓑ{a,I} V2. U2. /2 width=3 by lift_inv_bind1_aux/ qed-. -fact lift_inv_flat1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → +fact lift_inv_flat1_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀I,V1,U1. T1 = ⓕ{I} V1.U1 → - ∃∃V2,U2. ⇧[d,e] V1 ≡ V2 & ⇧[d,e] U1 ≡ U2 & + ∃∃V2,U2. ⬆[d,e] V1 ≡ V2 & ⬆[d,e] U1 ≡ U2 & T2 = ⓕ{I} V2. U2. #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #I #V1 #U1 #H destruct @@ -128,12 +128,12 @@ fact lift_inv_flat1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ] qed-. -lemma lift_inv_flat1: ∀d,e,T2,I,V1,U1. ⇧[d,e] ⓕ{I} V1. U1 ≡ T2 → - ∃∃V2,U2. ⇧[d,e] V1 ≡ V2 & ⇧[d,e] U1 ≡ U2 & +lemma lift_inv_flat1: ∀d,e,T2,I,V1,U1. ⬆[d,e] ⓕ{I} V1. U1 ≡ T2 → + ∃∃V2,U2. ⬆[d,e] V1 ≡ V2 & ⬆[d,e] U1 ≡ U2 & T2 = ⓕ{I} V2. U2. /2 width=3 by lift_inv_flat1_aux/ qed-. -fact lift_inv_sort2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k → T1 = ⋆k. +fact lift_inv_sort2_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k → T1 = ⋆k. #d #e #T1 #T2 * -d -e -T1 -T2 // [ #i #d #e #_ #k #H destruct | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct @@ -142,10 +142,10 @@ fact lift_inv_sort2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k qed-. (* Basic_1: was: lift_gen_sort *) -lemma lift_inv_sort2: ∀d,e,T1,k. ⇧[d,e] T1 ≡ ⋆k → T1 = ⋆k. +lemma lift_inv_sort2: ∀d,e,T1,k. ⬆[d,e] T1 ≡ ⋆k → T1 = ⋆k. /2 width=5 by lift_inv_sort2_aux/ qed-. -fact lift_inv_lref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T2 = #i → +fact lift_inv_lref2_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀i. T2 = #i → (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)). #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #i #H destruct @@ -158,12 +158,12 @@ fact lift_inv_lref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T2 = #i → qed-. (* Basic_1: was: lift_gen_lref *) -lemma lift_inv_lref2: ∀d,e,T1,i. ⇧[d,e] T1 ≡ #i → +lemma lift_inv_lref2: ∀d,e,T1,i. ⬆[d,e] T1 ≡ #i → (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)). /2 width=3 by lift_inv_lref2_aux/ qed-. (* Basic_1: was: lift_gen_lref_lt *) -lemma lift_inv_lref2_lt: ∀d,e,T1,i. ⇧[d,e] T1 ≡ #i → i < d → T1 = #i. +lemma lift_inv_lref2_lt: ∀d,e,T1,i. ⬆[d,e] T1 ≡ #i → i < d → T1 = #i. #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H * // #Hdi #_ #Hid lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd elim (lt_inv_plus_l … Hdd) -Hdd #Hdd @@ -171,7 +171,7 @@ elim (lt_refl_false … Hdd) qed-. (* Basic_1: was: lift_gen_lref_false *) -lemma lift_inv_lref2_be: ∀d,e,T1,i. ⇧[d,e] T1 ≡ #i → +lemma lift_inv_lref2_be: ∀d,e,T1,i. ⬆[d,e] T1 ≡ #i → d ≤ i → i < d + e → ⊥. #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H * [ #H1 #_ #H2 #_ | #H2 #_ #_ #H1 ] @@ -180,14 +180,14 @@ elim (lt_refl_false … H) qed-. (* Basic_1: was: lift_gen_lref_ge *) -lemma lift_inv_lref2_ge: ∀d,e,T1,i. ⇧[d,e] T1 ≡ #i → d + e ≤ i → T1 = #(i - e). +lemma lift_inv_lref2_ge: ∀d,e,T1,i. ⬆[d,e] T1 ≡ #i → d + e ≤ i → T1 = #(i - e). #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H * // #Hid #_ #Hdi lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd elim (lt_inv_plus_l … Hdd) -Hdd #Hdd elim (lt_refl_false … Hdd) qed-. -fact lift_inv_gref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T2 = §p → T1 = §p. +fact lift_inv_gref2_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀p. T2 = §p → T1 = §p. #d #e #T1 #T2 * -d -e -T1 -T2 // [ #i #d #e #_ #k #H destruct | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct @@ -195,12 +195,12 @@ fact lift_inv_gref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T2 = §p → ] qed-. -lemma lift_inv_gref2: ∀d,e,T1,p. ⇧[d,e] T1 ≡ §p → T1 = §p. +lemma lift_inv_gref2: ∀d,e,T1,p. ⬆[d,e] T1 ≡ §p → T1 = §p. /2 width=5 by lift_inv_gref2_aux/ qed-. -fact lift_inv_bind2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → +fact lift_inv_bind2_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀a,I,V2,U2. T2 = ⓑ{a,I} V2.U2 → - ∃∃V1,U1. ⇧[d,e] V1 ≡ V2 & ⇧[d+1,e] U1 ≡ U2 & + ∃∃V1,U1. ⬆[d,e] V1 ≡ V2 & ⬆[d+1,e] U1 ≡ U2 & T1 = ⓑ{a,I} V1. U1. #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #a #I #V2 #U2 #H destruct @@ -213,14 +213,14 @@ fact lift_inv_bind2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → qed-. (* Basic_1: was: lift_gen_bind *) -lemma lift_inv_bind2: ∀d,e,T1,a,I,V2,U2. ⇧[d,e] T1 ≡ ⓑ{a,I} V2. U2 → - ∃∃V1,U1. ⇧[d,e] V1 ≡ V2 & ⇧[d+1,e] U1 ≡ U2 & +lemma lift_inv_bind2: ∀d,e,T1,a,I,V2,U2. ⬆[d,e] T1 ≡ ⓑ{a,I} V2. U2 → + ∃∃V1,U1. ⬆[d,e] V1 ≡ V2 & ⬆[d+1,e] U1 ≡ U2 & T1 = ⓑ{a,I} V1. U1. /2 width=3 by lift_inv_bind2_aux/ qed-. -fact lift_inv_flat2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → +fact lift_inv_flat2_aux: ∀d,e,T1,T2. ⬆[d,e] T1 ≡ T2 → ∀I,V2,U2. T2 = ⓕ{I} V2.U2 → - ∃∃V1,U1. ⇧[d,e] V1 ≡ V2 & ⇧[d,e] U1 ≡ U2 & + ∃∃V1,U1. ⬆[d,e] V1 ≡ V2 & ⬆[d,e] U1 ≡ U2 & T1 = ⓕ{I} V1. U1. #d #e #T1 #T2 * -d -e -T1 -T2 [ #k #d #e #I #V2 #U2 #H destruct @@ -233,12 +233,12 @@ fact lift_inv_flat2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → qed-. (* Basic_1: was: lift_gen_flat *) -lemma lift_inv_flat2: ∀d,e,T1,I,V2,U2. ⇧[d,e] T1 ≡ ⓕ{I} V2. U2 → - ∃∃V1,U1. ⇧[d,e] V1 ≡ V2 & ⇧[d,e] U1 ≡ U2 & +lemma lift_inv_flat2: ∀d,e,T1,I,V2,U2. ⬆[d,e] T1 ≡ ⓕ{I} V2. U2 → + ∃∃V1,U1. ⬆[d,e] V1 ≡ V2 & ⬆[d,e] U1 ≡ U2 & T1 = ⓕ{I} V1. U1. /2 width=3 by lift_inv_flat2_aux/ qed-. -lemma lift_inv_pair_xy_x: ∀d,e,I,V,T. ⇧[d, e] ②{I} V. T ≡ V → ⊥. +lemma lift_inv_pair_xy_x: ∀d,e,I,V,T. ⬆[d, e] ②{I} V. T ≡ V → ⊥. #d #e #J #V elim V -V [ * #i #T #H [ lapply (lift_inv_sort2 … H) -H #H destruct @@ -253,7 +253,7 @@ lemma lift_inv_pair_xy_x: ∀d,e,I,V,T. ⇧[d, e] ②{I} V. T ≡ V → ⊥. qed-. (* Basic_1: was: thead_x_lift_y_y *) -lemma lift_inv_pair_xy_y: ∀I,T,V,d,e. ⇧[d, e] ②{I} V. T ≡ T → ⊥. +lemma lift_inv_pair_xy_y: ∀I,T,V,d,e. ⬆[d, e] ②{I} V. T ≡ T → ⊥. #J #T elim T -T [ * #i #V #d #e #H [ lapply (lift_inv_sort2 … H) -H #H destruct @@ -269,33 +269,33 @@ qed-. (* Basic forward lemmas *****************************************************) -lemma lift_fwd_pair1: ∀I,T2,V1,U1,d,e. ⇧[d,e] ②{I}V1.U1 ≡ T2 → - ∃∃V2,U2. ⇧[d,e] V1 ≡ V2 & T2 = ②{I}V2.U2. +lemma lift_fwd_pair1: ∀I,T2,V1,U1,d,e. ⬆[d,e] ②{I}V1.U1 ≡ T2 → + ∃∃V2,U2. ⬆[d,e] V1 ≡ V2 & T2 = ②{I}V2.U2. * [ #a ] #I #T2 #V1 #U1 #d #e #H [ elim (lift_inv_bind1 … H) -H /2 width=4 by ex2_2_intro/ | elim (lift_inv_flat1 … H) -H /2 width=4 by ex2_2_intro/ ] qed-. -lemma lift_fwd_pair2: ∀I,T1,V2,U2,d,e. ⇧[d,e] T1 ≡ ②{I}V2.U2 → - ∃∃V1,U1. ⇧[d,e] V1 ≡ V2 & T1 = ②{I}V1.U1. +lemma lift_fwd_pair2: ∀I,T1,V2,U2,d,e. ⬆[d,e] T1 ≡ ②{I}V2.U2 → + ∃∃V1,U1. ⬆[d,e] V1 ≡ V2 & T1 = ②{I}V1.U1. * [ #a ] #I #T1 #V2 #U2 #d #e #H [ elim (lift_inv_bind2 … H) -H /2 width=4 by ex2_2_intro/ | elim (lift_inv_flat2 … H) -H /2 width=4 by ex2_2_intro/ ] qed-. -lemma lift_fwd_tw: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → ♯{T1} = ♯{T2}. +lemma lift_fwd_tw: ∀d,e,T1,T2. ⬆[d, e] T1 ≡ T2 → ♯{T1} = ♯{T2}. #d #e #T1 #T2 #H elim H -d -e -T1 -T2 normalize // qed-. -lemma lift_simple_dx: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄. +lemma lift_simple_dx: ∀d,e,T1,T2. ⬆[d, e] T1 ≡ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄. #d #e #T1 #T2 #H elim H -d -e -T1 -T2 // #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #H elim (simple_inv_bind … H) qed-. -lemma lift_simple_sn: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄. +lemma lift_simple_sn: ∀d,e,T1,T2. ⬆[d, e] T1 ≡ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄. #d #e #T1 #T2 #H elim H -d -e -T1 -T2 // #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #H elim (simple_inv_bind … H) @@ -304,22 +304,22 @@ qed-. (* Basic properties *********************************************************) (* Basic_1: was: lift_lref_gt *) -lemma lift_lref_ge_minus: ∀d,e,i. d + e ≤ i → ⇧[d, e] #(i - e) ≡ #i. +lemma lift_lref_ge_minus: ∀d,e,i. d + e ≤ i → ⬆[d, e] #(i - e) ≡ #i. #d #e #i #H >(plus_minus_m_m i e) in ⊢ (? ? ? ? %); /3 width=2 by lift_lref_ge, le_plus_to_minus_r, le_plus_b/ qed. -lemma lift_lref_ge_minus_eq: ∀d,e,i,j. d + e ≤ i → j = i - e → ⇧[d, e] #j ≡ #i. +lemma lift_lref_ge_minus_eq: ∀d,e,i,j. d + e ≤ i → j = i - e → ⬆[d, e] #j ≡ #i. /2 width=1/ qed-. (* Basic_1: was: lift_r *) -lemma lift_refl: ∀T,d. ⇧[d, 0] T ≡ T. +lemma lift_refl: ∀T,d. ⬆[d, 0] T ≡ T. #T elim T -T [ * #i // #d elim (lt_or_ge i d) /2 width=1 by lift_lref_lt, lift_lref_ge/ | * /2 width=1 by lift_bind, lift_flat/ ] qed. -lemma lift_total: ∀T1,d,e. ∃T2. ⇧[d,e] T1 ≡ T2. +lemma lift_total: ∀T1,d,e. ∃T2. ⬆[d,e] T1 ≡ T2. #T1 elim T1 -T1 [ * #i /2 width=2/ #d #e elim (lt_or_ge i d) /3 width=2 by lift_lref_lt, lift_lref_ge, ex_intro/ | * [ #a ] #I #V1 #T1 #IHV1 #IHT1 #d #e @@ -331,9 +331,9 @@ lemma lift_total: ∀T1,d,e. ∃T2. ⇧[d,e] T1 ≡ T2. qed. (* Basic_1: was: lift_free (right to left) *) -lemma lift_split: ∀d1,e2,T1,T2. ⇧[d1, e2] T1 ≡ T2 → +lemma lift_split: ∀d1,e2,T1,T2. ⬆[d1, e2] T1 ≡ T2 → ∀d2,e1. d1 ≤ d2 → d2 ≤ d1 + e1 → e1 ≤ e2 → - ∃∃T. ⇧[d1, e1] T1 ≡ T & ⇧[d2, e2 - e1] T ≡ T2. + ∃∃T. ⬆[d1, e1] T1 ≡ T & ⬆[d2, e2 - e1] T ≡ T2. #d1 #e2 #T1 #T2 #H elim H -d1 -e2 -T1 -T2 [ /3 width=3/ | #i #d1 #e2 #Hid1 #d2 #e1 #Hd12 #_ #_ @@ -352,7 +352,7 @@ lemma lift_split: ∀d1,e2,T1,T2. ⇧[d1, e2] T1 ≡ T2 → qed. (* Basic_1: was only: dnf_dec2 dnf_dec *) -lemma is_lift_dec: ∀T2,d,e. Decidable (∃T1. ⇧[d,e] T1 ≡ T2). +lemma is_lift_dec: ∀T2,d,e. Decidable (∃T1. ⬆[d,e] T1 ≡ T2). #T1 elim T1 -T1 [ * [1,3: /3 width=2 by lift_sort, lift_gref, ex_intro, or_introl/ ] #i #d #e elim (lt_or_ge i d) #Hdi