/2/ qed.
lemma cpr_tps: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → L ⊢ T1 ⇒ T2.
-/3 width=5/ qed.
+/3 width=5/ qed.
lemma cpr_refl: ∀L,T. L ⊢ T ⇒ T.
/2/ qed.
#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/
qed.
-lemma cpr_delta: ∀L,K,V1,V2,V,i.
- ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫ V2 →
- ↑[0, i + 1] V2 ≡ V → L ⊢ #i ⇒ V.
-#L #K #V1 #V2 #V #i #HLK #HV12 #HV2
-@ex2_1_intro [2: // | skip ] /3 width=8/ (**) (* /4/ is too slow *)
+lemma cpr_delta: ∀L,K,V,W,i.
+ ↓[0, i] L ≡ K. 𝕓{Abbr} V → ↑[0, i + 1] V ≡ W → L ⊢ #i ⇒ W.
+/3/
qed.
lemma cpr_cast: ∀L,V,T1,T2.
inductive lcpr: lenv → lenv → Prop ≝
| lcpr_sort: lcpr (⋆) (⋆)
| lcpr_item: ∀K1,K2,I,V1,V2.
- lcpr K1 K2 → K1 ⊢ V1 ⇒ V2 → lcpr (K1. 𝕓{I} V1) (K2. 𝕓{I} V2) (*𝕓*)
+ lcpr K1 K2 → K2 ⊢ V1 ⇒ V2 → lcpr (K1. 𝕓{I} V1) (K2. 𝕓{I} V2) (*𝕓*)
.
interpretation
(* Basic inversion lemmas ***************************************************)
lemma lcpr_inv_item1_aux: ∀L1,L2. L1 ⊢ ⇒ L2 → ∀K1,I,V1. L1 = K1. 𝕓{I} V1 →
- ∃∃K2,V2. K1 ⊢ ⇒ K2 & K1 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
+ ∃∃K2,V2. K1 ⊢ ⇒ K2 & K2 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
#L1 #L2 * -L1 L2
[ #K1 #I #V1 #H destruct
| #K1 #K2 #I #V1 #V2 #HK12 #HV12 #L #J #W #H destruct - K1 I V1 /2 width=5/
qed.
lemma lcpr_inv_item1: ∀K1,I,V1,L2. K1. 𝕓{I} V1 ⊢ ⇒ L2 →
- ∃∃K2,V2. K1 ⊢ ⇒ K2 & K1 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
+ ∃∃K2,V2. K1 ⊢ ⇒ K2 & K2 ⊢ V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
/2/ qed.
include "Basic-2/substitution/drop.ma".
-(* PARTIAL SUBSTITUTION ON TERMS ********************************************)
+(* PARALLEL SUBSTITUTION ON TERMS *******************************************)
inductive tps: lenv → term → nat → nat → term → Prop ≝
| tps_sort : ∀L,k,d,e. tps L (⋆k) d e (⋆k)
| tps_lref : ∀L,i,d,e. tps L (#i) d e (#i)
-| tps_subst: ∀L,K,V,U1,U2,i,d,e.
- d ≤ i → i < d + e →
- ↓[0, i] L ≡ K. 𝕓{Abbr} V → tps K V 0 (d + e - i - 1) U1 →
- ↑[0, i + 1] U1 ≡ U2 → tps L (#i) d e U2
+| tps_subst: ∀L,K,V,W,i,d,e. d ≤ i → i < d + e →
+ ↓[0, i] L ≡ K. 𝕓{Abbr} V → ↑[0, i + 1] V ≡ W → tps L (#i) d e W
| tps_bind : ∀L,I,V1,V2,T1,T2,d,e.
tps L V1 d e V2 → tps (L. 𝕓{I} V1) T1 (d + 1) e T2 →
tps L (𝕓{I} V1. T1) d e (𝕓{I} V2. T2)
tps L (𝕗{I} V1. T1) d e (𝕗{I} V2. T2)
.
-interpretation "partial telescopic substritution"
+interpretation "parallel substritution (term)"
'PSubst L T1 d e T2 = (tps L T1 d e T2).
(* Basic properties *********************************************************)
#L1 #T1 #T2 #d #e #H elim H -H L1 T1 T2 d e
[ //
| //
-| #L1 #K1 #V #V1 #V2 #i #d #e #Hdi #Hide #HLK1 #_ #HV12 #IHV12 #L2 #HL12
- elim (drop_leq_drop1 … HL12 … HLK1 ? ?) -HL12 HLK1 // #K2 #HK12 #HLK2
- @tps_subst [4,5,6,8: // |1,2,3: skip | /2/ ] (**) (* /3 width=6/ is too slow *)
+| #L1 #K1 #V #W #i #d #e #Hdi #Hide #HLK1 #HVW #L2 #HL12
+ elim (drop_leq_drop1 … HL12 … HLK1 ? ?) -HL12 HLK1 // /2/
| /4/
| /3/
]
#L #T1 #T #d1 #e1 #H elim H -L T1 T d1 e1
[ //
| //
-| #L #K #V #V1 #V2 #i #d1 #e1 #Hid1 #Hide1 #HLK #_ #HV12 #IHV12 #d2 #e2 #Hd12 #Hde12
+| #L #K #V #W #i #d1 #e1 #Hid1 #Hide1 #HLK #HVW #d2 #e2 #Hd12 #Hde12
lapply (transitive_le … Hd12 … Hid1) -Hd12 Hid1 #Hid2
- lapply (lt_to_le_to_lt … Hide1 … Hde12) -Hide1 #Hide2
- @tps_subst [4,5,6,8: // |1,2,3: skip | @IHV12 /2/ ] (**) (* /4 width=6/ is too slow *)
+ lapply (lt_to_le_to_lt … Hide1 … Hde12) -Hide1 /2/
| /4/
| /4/
]
#L #T1 #T #d #e #H elim H -L T1 T d e
[ //
| //
-| #L #K #V #V1 #V2 #i #d #e #Hdi #_ #HLK #_ #HV12 #IHV12
+| #L #K #V #W #i #d #e #Hdi #_ #HLK #HVW
lapply (drop_fwd_drop2_length … HLK) #Hi
lapply (le_to_lt_to_lt … Hdi Hi) #Hd
- lapply (plus_minus_m_m_comm (|L|) d ?) [ /2/ ] -Hd #Hd
- lapply (drop_fwd_O1_length … HLK) normalize #HKL
- lapply (tps_weak … IHV12 0 (|L| - i - 1) ? ?) -IHV12 // -HKL /2 width=6/
+ lapply (plus_minus_m_m_comm (|L|) d ?) /2/
| normalize /2/
| /2/
]
#L #T1 #T #d #e #HT12
lapply (tps_weak … HT12 0 (d + e) ? ?) -HT12 // #HT12
lapply (tps_weak_top … HT12) //
-qed.
+qed.
(* Basic inversion lemmas ***************************************************)
lemma tps_inv_lref1_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → ∀i. T1 = #i →
T2 = #i ∨
- ∃∃K,V1,V2,i. d ≤ i & i < d + e &
- ↓[O, i] L ≡ K. 𝕓{Abbr} V1 &
- K ⊢ V1 [O, d + e - i - 1] ≫ V2 &
- ↑[O, i + 1] V2 ≡ T2.
+ ∃∃K,V,i. d ≤ i & i < d + e &
+ ↓[O, i] L ≡ K. 𝕓{Abbr} V &
+ ↑[O, i + 1] V ≡ T2.
#L #T1 #T2 #d #e * -L T1 T2 d e
[ #L #k #d #e #i #H destruct
| /2/
-| #L #K #V1 #V2 #T2 #i #d #e #Hdi #Hide #HLK #HV12 #HVT2 #j #H destruct -i /3 width=9/
+| #L #K #V #T2 #i #d #e #Hdi #Hide #HLK #HVT2 #j #H destruct -i /3 width=7/
| #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
| #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
]
lemma tps_inv_lref1: ∀L,T2,i,d,e. L ⊢ #i [d, e] ≫ T2 →
T2 = #i ∨
- ∃∃K,V1,V2,i. d ≤ i & i < d + e &
- ↓[O, i] L ≡ K. 𝕓{Abbr} V1 &
- K ⊢ V1 [O, d + e - i - 1] ≫ V2 &
- ↑[O, i + 1] V2 ≡ T2.
+ ∃∃K,V,i. d ≤ i & i < d + e &
+ ↓[O, i] L ≡ K. 𝕓{Abbr} V &
+ ↑[O, i + 1] V ≡ T2.
/2/ qed.
lemma tps_inv_bind1_aux: ∀d,e,L,U1,U2. L ⊢ U1 [d, e] ≫ U2 →
#d #e #L #U1 #U2 * -d e L U1 U2
[ #L #k #d #e #I #V1 #T1 #H destruct
| #L #i #d #e #I #V1 #T1 #H destruct
-| #L #K #V #U1 #U2 #i #d #e #_ #_ #_ #_ #_ #I #V1 #T1 #H destruct
+| #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct
| #L #J #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #I #V #T #H destruct /2 width=5/
| #L #J #V1 #V2 #T1 #T2 #d #e #_ #_ #I #V #T #H destruct
]
#d #e #L #U1 #U2 * -d e L U1 U2
[ #L #k #d #e #I #V1 #T1 #H destruct
| #L #i #d #e #I #V1 #T1 #H destruct
-| #L #K #V #U1 #U2 #i #d #e #_ #_ #_ #_ #_ #I #V1 #T1 #H destruct
+| #L #K #V #W #i #d #e #_ #_ #_ #_ #I #V1 #T1 #H destruct
| #L #J #V1 #V2 #T1 #T2 #d #e #_ #_ #I #V #T #H destruct
| #L #J #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #I #V #T #H destruct /2 width=5/
]
L ⊢ U1 [dt, et] ≫ U2.
#K #T1 #T2 #dt #et #H elim H -H K T1 T2 dt et
[ #K #k #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_
- lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 //
+ >(lift_mono … H1 … H2) -H1 H2 //
| #K #i #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_
- lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 //
-| #K #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HKV #_ #HV12 #IHV12 #L #U1 #U2 #d #e #HLK #H #HVU2 #Hdetd
- lapply (lt_to_le_to_lt … Hidet … Hdetd) #Hid
+ >(lift_mono … H1 … H2) -H1 H2 //
+| #K #KV #V #W #i #dt #et #Hdti #Hidet #HKV #HVW #L #U1 #U2 #d #e #HLK #H #HVU2 #Hdetd
+ lapply (lt_to_le_to_lt … Hidet … Hdetd) -Hdetd #Hid
lapply (lift_inv_lref1_lt … H … Hid) -H #H destruct -U1;
- elim (lift_trans_ge … HV12 … HVU2 ?) -HV12 HVU2 V2 // <minus_plus #V2 #HV12 #HVU2
- elim (drop_trans_le … HLK … HKV ?) -HLK HKV K /2/ #X #HLK #H
- elim (drop_inv_skip2 … H ?) -H /2/ -Hid #K #W #HKV #HVW #H destruct -X
- @tps_subst [4,5,6,8: // |1,2,3: skip | @IHV12 /2 width=6/ ] (**) (* explicit constructor *)
+ elim (lift_trans_ge … HVW … HVU2 ?) -HVW HVU2 W // <minus_plus #W #HVW #HWU2
+ elim (drop_trans_le … HLK … HKV ?) -HLK HKV K [2: /2/] #X #HLK #H
+ elim (drop_inv_skip2 … H ?) -H [2: /2/] -Hid #K #Y #_ #HVY
+ >(lift_mono … HVY … HVW) -HVY HVW Y #H destruct -X /2/
| #K #I #V1 #V2 #T1 #T2 #dt #et #_ #_ #IHV12 #IHT12 #L #U1 #U2 #d #e #HLK #H1 #H2 #Hdetd
elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1
elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct -U1 U2;
L ⊢ U1 [dt + e, et] ≫ U2.
#K #T1 #T2 #dt #et #H elim H -H K T1 T2 dt et
[ #K #k #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_
- lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 //
+ >(lift_mono … H1 … H2) -H1 H2 //
| #K #i #dt #et #L #U1 #U2 #d #e #_ #H1 #H2 #_
- lapply (lift_mono … H1 … H2) -H1 H2 #H destruct -U1 //
-| #K #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HKV #HV1 #HV12 #_ #L #U1 #U2 #d #e #HLK #H #HVU2 #Hddt
- <(arith_c1x ? ? ? e) in HV1 #HV1 (**) (* explicit athmetical rewrite and ?'s *)
+ >(lift_mono … H1 … H2) -H1 H2 //
+| #K #KV #V #W #i #dt #et #Hdti #Hidet #HKV #HVW #L #U1 #U2 #d #e #HLK #H #HWU2 #Hddt
lapply (transitive_le … Hddt … Hdti) -Hddt #Hid
lapply (lift_inv_lref1_ge … H … Hid) -H #H destruct -U1;
- lapply (lift_trans_be … HV12 … HVU2 ? ?) -HV12 HVU2 V2 /2/ >plus_plus_comm_23 #HV1U2
- lapply (drop_trans_ge_comm … HLK … HKV ?) -HLK HKV K // -Hid #HLKV
- @tps_subst [4,5: /2/ |6,7,8: // |1,2,3: skip ] (**) (* /3 width=8/ is too slow *)
+ lapply (lift_trans_be … HVW … HWU2 ? ?) -HVW HWU2 W // [ /2/ ] >plus_plus_comm_23 #HVU2
+ lapply (drop_trans_ge_comm … HLK … HKV ?) -HLK HKV K // -Hid /3/
| #K #I #V1 #V2 #T1 #T2 #dt #et #_ #_ #IHV12 #IHT12 #L #U1 #U2 #d #e #HLK #H1 #H2 #Hddt
elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1
elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct -U1 U2;
lapply (lift_inv_sort2 … H) -H #H destruct -T1 /2/
| #L #i #dt #et #K #d #e #_ #T1 #H #_
elim (lift_inv_lref2 … H) -H * #Hid #H destruct -T1 /3/
-| #L #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HLKV #_ #HV12 #IHV12 #K #d #e #HLK #T1 #H #Hdetd
- lapply (lt_to_le_to_lt … Hidet … Hdetd) #Hid
+| #L #KV #V #W #i #dt #et #Hdti #Hidet #HLKV #HVW #K #d #e #HLK #T1 #H #Hdetd
+ lapply (lt_to_le_to_lt … Hidet … Hdetd) -Hdetd #Hid
lapply (lift_inv_lref2_lt … H … Hid) -H #H destruct -T1;
- elim (drop_conf_lt … HLK … HLKV ?) -HLK HLKV L // #L #W #HKL #HKVL #HWV
- elim (IHV12 … HKVL … HWV ?) -HKVL HWV /2/ -Hdetd #W1 #HW1 #HWV1
- elim (lift_trans_le … HWV1 … HV12 ?) -HWV1 HV12 V1 // >arith_a2 /3 width=6/
+ elim (drop_conf_lt … HLK … HLKV ?) -HLK HLKV L // #L #U #HKL #_ #HUV
+ elim (lift_trans_le … HUV … HVW ?) -HUV HVW V // >arith_a2 // -Hid /3/
| #L #I #V1 #V2 #U1 #U2 #dt #et #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H #Hdetd
elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct -X;
elim (IHV12 … HLK … HWV1 ?) -IHV12 //
lapply (lift_inv_sort2 … H) -H #H destruct -T1 /2/
| #L #i #dt #et #K #d #e #_ #T1 #H #_
elim (lift_inv_lref2 … H) -H * #Hid #H destruct -T1 /3/
-| #L #KV #V #V1 #V2 #i #dt #et #Hdti #Hidet #HLKV #HV1 #HV12 #_ #K #d #e #HLK #T1 #H #Hdedt
+| #L #KV #V #W #i #dt #et #Hdti #Hidet #HLKV #HVW #K #d #e #HLK #T1 #H #Hdedt
lapply (transitive_le … Hdedt … Hdti) #Hdei
lapply (plus_le_weak … Hdedt) -Hdedt #Hedt
- lapply (plus_le_weak … Hdei) #Hei
- <(arith_h1 ? ? ? e ? ?) in HV1 // #HV1
+ lapply (plus_le_weak … Hdei) #Hei
lapply (lift_inv_lref2_ge … H … Hdei) -H #H destruct -T1;
lapply (drop_conf_ge … HLK … HLKV ?) -HLK HLKV L // #HKV
- elim (lift_split … HV12 d (i - e + 1) ? ? ?) -HV12; [2,3,4: normalize /2/ ] -Hdei >arith_e2 // #V0 #HV10 #HV02
+ elim (lift_split … HVW d (i - e + 1) ? ? ?) -HVW; [2,3,4: normalize /2/ ] -Hdei >arith_e2 // #V0 #HV10 #HV02
@ex2_1_intro
- [2: @tps_subst [4: /2/ |6,7,8: // |1,2,3: skip |5: @arith5 // ]
+ [2: @tps_subst [3: /2/ |5,6: // |1,2: skip |4: @arith5 // ]
|1: skip
| //
] (**) (* explicitc constructors *)
#L #U1 #U2 #d #e #H elim H -H L U1 U2 d e
[ //
| //
-| #L #K #V #V1 #V2 #i #d #e #Hdi #Hide #_ #_ #_ #_ #T1 #H
+| #L #K #V #W #i #d #e #Hdi #Hide #_ #_ #T1 #H
elim (lift_inv_lref2 … H) -H * #H
[ lapply (le_to_lt_to_lt … Hdi … H) -Hdi H #H
elim (lt_refl_false … H)
#L #T1 #T2 #d #e #H elim H -L T1 T2 d e
[ /2/
| /2/
-| #L #K #V #V1 #V2 #i #d #e #Hdi #Hide #HLK #HV1 #HV12 #IHV12 #j #Hdj #Hjde
- elim (lt_or_ge i j) #Hij
- [ -HV1 Hide;
- lapply (drop_fwd_drop2 … HLK) #HLK'
- elim (IHV12 (j - i - 1) ? ?) -IHV12; normalize /2/ -Hjde <minus_n_O >arith_b2 // #W1 #HVW1 #HWV1
- generalize in match HVW1 generalize in match Hij -HVW1 (**) (* rewriting in the premises, rewrites in the goal too *)
- >(plus_minus_m_m_comm … Hdj) in ⊢ (% → % → ?) -Hdj #Hij' #HVW1
- elim (lift_total W1 0 (i + 1)) #W2 #HW12
- lapply (tps_lift_ge … HWV1 … HLK' HW12 HV12 ?) -HWV1 HLK' HV12 // >arith_a2 /3 width=6/
- | -IHV12 Hdi Hdj;
- generalize in match HV1 generalize in match Hide -HV1 Hide (**) (* rewriting in the premises, rewrites in the goal too *)
- >(plus_minus_m_m_comm … Hjde) in ⊢ (% → % → ?) -Hjde #Hide #HV1
- @ex2_1_intro [2: @tps_lref |1: skip | /2 width=6/ ] (**) (* /3 width=6 is too slow *)
+| #L #K #V #W #i #d #e #Hdi #Hide #HLK #HVW #j #Hdj #Hjde
+ elim (lt_or_ge i j)
+ [ -Hide Hjde;
+ >(plus_minus_m_m_comm j d) in ⊢ (% → ?) // -Hdj /3/
+ | -Hdi Hdj; #Hid
+ generalize in match Hide -Hide (**) (* rewriting in the premises, rewrites in the goal too *)
+ >(plus_minus_m_m_comm … Hjde) in ⊢ (% → ?) -Hjde /4/
]
| #L #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #i #Hdi #Hide
elim (IHV12 i ? ?) -IHV12 // #V #HV1 #HV2
qed.
*)
-axiom tps_conf_subst_subst_lt: ∀L,K1,V1,W1,T1,i1,d,e,T2,K2,V2,W2,i2.
+axiom tps_conf_subst_subst_lt: ∀L,K1,V1,T1,i1,d,e,T2,K2,V2,i2.
↓[O, i1] L ≡ K1. 𝕓{Abbr} V1 → ↓[O, i2] L≡ K2. 𝕓{Abbr} V2 →
- K1 ⊢ V1 [O, d + e - i1 - 1] ≫ W1 → K2 ⊢ V2 [O, d + e - i2 - 1] ≫ W2 →
- ↑[O, i1 + 1] W1 ≡ T1 → ↑[O, i2 + 1] W2 ≡ T2 →
+ ↑[O, i1 + 1] V1 ≡ T1 → ↑[O, i2 + 1] V2 ≡ T2 →
d ≤ i1 → i1 < d + e → d ≤ i2 → i2 < d + e → i1 < i2 →
∃∃T. L ⊢ T1 [d, e] ≫ T & L ⊢ T2 [d, e] ≫ T.
(*
-#L #K1 #V1 #W1 #T1 #i1 #d #e #T2 #K2 #V2 #W2 #i2
+#L #K1 #V1 #T1 #i1 #d #e #T2 #K2 #V2 #i2
#HLK1 #HLK2 #HVW1 #HVW2 #HWT1 #HWT2 #Hdi1 #Hi1de #Hdi2 #Hi2de #Hi12
*)
#L #T0 #T1 #d #e #H elim H -H L T0 T1 d e
[ /2/
| /2/
-| #L #K1 #V1 #W1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVW1 #HWT1 #IHVW1 #T2 #H
+| #L #K1 #V1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVT1 #T2 #H
elim (tps_inv_lref1 … H) -H
- [ -IHVW1 #HX destruct -T2
- @ex2_1_intro [2: // | skip ] /2 width=6/ (**) (* /3 width=9/ is slow *)
- | * #K2 #V2 #W2 #i2 #Hdi2 #Hi2de #HLK2 #HVW2 #HWT2
+ [ #HX destruct -T2 /4/
+ | * #K2 #V2 #i2 #Hdi2 #Hi2de #HLK2 #HVT2
elim (lt_or_eq_or_gt i1 i2) #Hi12
- [ @tps_conf_subst_subst_lt /width=19/
- | -HVW1; destruct -i2;
- lapply (transitive_le ? ? (i1 + 1) Hdi2 ?) -Hdi2 // #Hdi2
- lapply (drop_mono … HLK1 … HLK2) -HLK1 Hdi1 Hi1de #H destruct -V1 K1;
- elim (IHVW1 … HVW2) -IHVW1 HVW2 #W #HW1 #HW2
- lapply (drop_fwd_drop2 … HLK2) -HLK2 #HLK2
- elim (lift_total W 0 (i1 + 1)) #T #HWT
- lapply (tps_lift_ge … HW1 … HLK2 HWT1 HWT ?) -HW1 HWT1 //
- lapply (tps_lift_ge … HW2 … HLK2 HWT2 HWT ?) -HW2 HWT2 HLK2 HWT // normalize #HT2 #HT1
- lapply (tps_weak … HT1 d e ? ?) -HT1 [ >arith_i2 // | // ]
- lapply (tps_weak … HT2 d e ? ?) -HT2 [ >arith_i2 // | // ]
- /2/
- | @ex2_1_comm @tps_conf_subst_subst_lt /width=19/
+ [ @tps_conf_subst_subst_lt /width=15/
+ | -Hdi2 Hi2de; destruct -i2;
+ lapply (drop_mono … HLK1 … HLK2) -HLK1 #H destruct -V1 K1
+ >(lift_mono … HVT1 … HVT2) -HVT1 /2/
+ | @ex2_1_comm @tps_conf_subst_subst_lt /width=15/
]
]
| #L #I #V0 #V1 #T0 #T1 #d #e #_ #_ #IHV01 #IHT01 #X #HX
projects / helm.git / commitdiff