+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/dynamic/snta_ltpss.ma".
-include "basic_2/dynamic/snta_thin.ma".
-include "basic_2/dynamic/lsubsn_snta.ma".
-
-(* STRATIFIED NATIVE TYPE ASSIGNMENT ON TERMS *******************************)
-(*
-lemma snta_fwd_abst: ∀h,L,W1,W2,T,U,l2. ⦃h, L⦄ ⊢ ⓛW1.T :[l2] ⓛW2.U →
- ∃∃V1,V2,l1. ⦃h, L⦄ ⊢ W1 :[l1] V1 & ⦃h, L⦄ ⊢ W2 :[l1] V2 &
- L ⊢ W1 ⬌* W2.
-#h #L #W1 #W2 #T #U #l2 #HTU
-elim (snta_fwd_correct … HTU) #X #H
-elim (snta_inv_bind1 … H) -H #W #T0 #l #HW2 #_ #_ -X
-elim (snta_inv_bind1 … HTU) -HTU #V1 #U0 #l0 #HWV1 #_ #H
-elim (cpcs_inv_abst … H Abst W1) -H
-#HW12 #_ -U0
-@(ex3_3_intro … HWV1 … HW12)
-[3: @(snta_conv … HTU0 HU0)
-
- /3 width=3/
-
-*)
-(*
-#h #L #V #T #U #l2 #HTU
-elim (snta_fwd_correct … HTU) #X #H
-elim (snta_inv_bind1 … H) -H #W #T0 #l1 #HVW #HUT0 #_ -X
-elim (snta_inv_bind1 … HTU) -HTU #W0 #U0 #l0 #_ #HTU0 #H -l0
-elim (cpcs_inv_abst … H Abst V) -H /3 width=3/
-qed-.
-*)
-(*
-lemma snta_fwd_appl1_sound_aux: ∀h,l0. (∀L1,L2,T1,T2,U,l.
- l < l0 → ⦃h, L1⦄ ⊢ T1 :[l] U →
- L1 ➡ L2 → L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 :[l] U
- ) →
- ∀L,T,U,l2. ⦃h, L⦄ ⊢ T :[l2] U →
- ∀Z,Y,X1. T = ⓐZ.ⓛY.X1 → l0 = l2 →
- ∃l1. ⦃h, L⦄ ⊢ Z :[l1+1] Y.
-#h #l0 #IH #L #T #U #l2 #H elim H -L -T -U -l2
-[
-|
-|
-|
-| #L #V #W1 #W2 #T #U #l1 #l2 #HVW2 #HTU #_ #_ #Z #Y #X1 #H1 #H2 destruct -IH
- elim (snta_fwd_abst … HTU) -X1 -U -l2 #Y0 #W0 #l0 #HY0 #H1 #HYW2
- elim (snta_fwd_correct … HVW2) #W #H2
- elim (snta_mono … H1 … H2) -H1 -H2 #H #_ destruct -W0 -W /4 width=6/
-| #L #V #T #U #W #l #HTU #HUW #Z #Y #X1 #X2 #H1 #H2 #H3 destruct
- elim (snta_inv_abst_sn … HTU) -HTU #Y0 #l0 #HY0 #HX12
-|
-| #L #T #U1 #U2 #V2 #l #HTU1 #HU12 #HUV2 #Z #Y #X1 #X2 #H1 #H2 #H3 destruct
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-lemma snta_inv_appl_aux: ∀h,l0. (∀L1,L2,T1,T2,U,l.
- l < l0 + 1 → ⦃h, L1⦄ ⊢ T1 :[l] U →
- L1 ➡ L2 → L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 :[l] U
- ) →
- ∀L,T,U,l2. ⦃h, L⦄ ⊢ T :[l2] U →
- ∀Z,Y,X1,X2. T = ⓐZ.ⓛY.X1 → U = ⓐZ.ⓛY.X2 → l0 = l2 →
- ∃∃l1. ⦃h, L⦄ ⊢ Z :[l1+1] Y & ⦃h, L.ⓛY⦄ ⊢ X1 :[l2] X2.
-#h #l0 #IH #L #T #U #l2 * -L -T -U -l2
-[
-|
-|
-|
-| #L #V #W1 #W2 #T #U #l1 #l2 #HVW2 #HTU #Z #Y #X1 #X2 #H1 #H2 #H3 destruct -IH
- elim (snta_inv_abst … HTU) -HTU /2 width=2/
-| #L #V #T #U #W #l #HTU #HUW #Z #Y #X1 #X2 #H1 #H2 #H3 destruct
- elim (snta_inv_abst … HTU) -HTU #Y0 #l0 #HY0 #HX12
-|
-| #L #T #U1 #U2 #V2 #l #HTU1 #HU12 #HUV2 #Z #Y #X1 #X2 #H1 #H2 #H3 destruct
-
- /2 width=2/
-
-
-axiom pippo: ∀h,l0. (∀L1,L2,T1,T2,U,l.
- l < l0 + 1 → ⦃h, L1⦄ ⊢ T1 :[l] U →
- L1 ➡ L2 → L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 :[l] U
- ) →
- ∀L,T1,U1,l. ⦃h, L⦄ ⊢ T1 :[l] U1 →
- ∀V2,W2,T2. L ⊢ T1 ➡* ⓐV2.ⓛW2.T2 → l0 = l →
- ∃l0. ⦃h, L2⦄ ⊢ V2 :[l0+1] W2.
-(*
-#h #l #IH #L1 #T1 #U1 #l1 * -L1 -T1 -U1 -l1
-[
-|
-|
-|
-| #L1 #V1 #W1 #T1 #U1 #l1 #HVW1 #HTU1 #Y1 #X1 #H1 #L2 #Y2 #HL12 #HY12 #Z2 #X2 #HX12 #H2 destruct
- elim (IH ??? Y2 … HVW1 HL12 ?) -HVW1 // [2: /3 width=1/ ] -HY12 #l21 #HY2W1 #H1l21 #H2l21
- elim (IH … HTU1 HL12 HX12) -IH -HTU1 -HL12 -HX12 // #l22 #H #_ #H2l22
- elim (snta_inv_bind1 … H) -H #Z #X #HZ2 #_ #H
- elim (cpcs_inv_abst … H Abst W1) -H #H #_
- lapply (transitive_le … (l21+l22) … H1l21 ?) -H1l21 // #Hl21
- @(ex3_1_intro … Hl21) [2: /3 width=1/ ]
- @(snta_conv … W1) /2 width=2/ (**) (* explicit constructors *)
-| #L1 #V1 #T1 #U1 #W1 #l1 #HTU1 #HUW1 #Y1 #X1 #H1 #L2 #Y2 #HL12 #HY12 #Z2 #X2 #HX12 #H2 destruct
-
-*)
-(* Properties on context-free parallel reduction for local environments *****)
-*)
-fact snta_ltpr_tpr_conf_aux: ∀h,l0. (∀L1,L2,T1,T2,U,l.
- l < l0 → ⦃h, L1⦄ ⊢ T1 :[l] U →
- L1 ➡ L2 → L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 :[l] U
- ) →
- ∀L1,T1,U,l. ⦃h, L1⦄ ⊢ T1 :[l] U → ∀L2. L1 ➡ L2 →
- ∀T2. T1 ➡ T2 → l0 = l → ⦃h, L2⦄ ⊢ T2 :[l] U.
-#h #l0 #IH #L1 #T1 #U #l #H elim H -L1 -T1 -U -l
-[ #L1 #k1 #L2 #_ #T2 #H #_ -l0
- >(tpr_inv_atom1 … H) -H //
-| #L1 #K1 #V1 #W #U #i1 #l #HLK1 #_ #HWU #IHV1 #L2 #HL12 #T2 #H #Hl -IH
- >(tpr_inv_atom1 … H) -T2
- elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #HLK2 #H
- elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct /3 width=6/
-| #L1 #K1 #W1 #V1 #U1 #i1 #l #HLK1 #HWV1 #HWU1 #IHWV1 #L2 #HL12 #T2 #H #Hl -IH
-(*
- >(tpr_inv_atom1 … H) -T2
- elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #HLK2 #H
- elim (ltpr_inv_pair1 … H) -H #K2 #W2 #HK12 #HW12 #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK2) #HLK
- elim (lift_total V1 0 (i+1)) #W #HW
- lapply (snta_lift h … HLK … HWU1 … HW) /2 width=1/ -HLK -HW
- elim (lift_total W2 0 (i+1)) #U2 #HWU2
- lapply (tpr_lift … HW12 … HWU1 … HWU2) -HWU1 #HU12
- @(snta_conv … U2) /2 width=1/ /3 width=6/ (**) (* explicit constructor, /3 width=6/ is too slow *)
-*)
-| #I #L1 #V1 #W1 #T1 #U1 #l1 #l2 #_ #_ #IHVW1 #IHTU1 #L2 #HL12 #X #H #Hl -IH
-(*
- elim (tpr_inv_bind1 … H) -H *
- [ #V2 #T #T2 #HV12 #HT1 #HT2 #H destruct
- lapply (IHVW1 … HL12 … HV12) #HV2W1
- lapply (IHVW1 L2 … V1 ?) // -IHVW1 #HWV1
- lapply (IHTU1 (L2.ⓑ{I}V2) … HT1) -HT1 /2 width=1/ #HTU1
- lapply (IHTU1 (L2.ⓑ{I}V1) ? T1 ?) -IHTU1 // /2 width=1/ -HL12 #H
- lapply (tps_lsubs_trans … HT2 (L2.ⓑ{I}V2) ?) -HT2 /2 width=1/ #HT2
- lapply (snta_tps_conf … HTU1 … HT2) -T #HT2U1
- elim (snta_fwd_correct … H) -H #U2 #HU12
- @(snta_conv … (ⓑ{I}V2.U1)) /2 width=2/ /3 width=1/ (**) (* explicit constructor, /4 width=6/ is too slow *)
- | #T #HT1 #HTX #H destruct
- lapply (IHVW1 … HL12 V1 ?) -IHVW1 // #HVW1
- lapply (IHTU1 (L2.ⓓV1) … HT1) -T1 /2 width=1/ -L1 #H
- elim (snta_fwd_correct … H) #T1 #HUT1
- elim (snta_ldrop_conf … H L2 0 1 ? ?) -H // /2 width=1/ #T0 #U0 #HTU0 #H #HU10
- lapply (delift_inv_lift1_eq … H L2 … HTX) -H -HTX /2 width=1/ #H destruct
- @(snta_conv … HTU0) /2 width=2/
- ]
-*)
-| #L1 #V1 #W11 #W2 #T1 #U1 #l1 #l2 #_ #_ #IHVW1 #IHTU1 #L2 #HL12 #X #H #Hl -IH
-(*
- elim (tpr_inv_appl1 … H) -H *
- [ #V2 #Y #HV12 #HY #H destruct
- elim (tpr_inv_abst1 … HY) -HY #W2 #T2 #HW12 #HT12 #H destruct
- lapply (IHTU1 L2 ? (ⓛW1.T1) ?) // #H
- elim (snta_fwd_correct … H) -H #X #H
- elim (snta_inv_bind1 … H) -H #W #U #HW #HU #_
- @(snta_conv … (ⓐV2.ⓛW1.U1)) /4 width=2/ (**) (* explicit constructor, /5 width=5/ is too slow *)
- | #V2 #W2 #T0 #T2 #HV12 #HT02 #H1 #H2 destruct
- lapply (IHVW1 … HL12 … HV12) #HVW2
- lapply (IHVW1 … HL12 V1 ?) -IHVW1 // #HV1W2
- lapply (IHTU1 … HL12 (ⓛW2.T2) ?) -IHTU1 -HL12 /2 width=1/ -HT02 #H1
- elim (snta_fwd_correct … H1) #T #H2
- elim (snta_inv_bind1 … H1) -H1 #W #U2 #HW2 #HTU2 #H
- elim (cpcs_inv_abst … H Abst W2) -H #_ #HU21
- elim (snta_inv_bind1 … H2) -H2 #W0 #U0 #_ #H #_ -T -W0
- lapply (lsubsn_snta_trans … HTU2 (L2.ⓓV2) ?) -HTU2 /2 width=1/ #HTU2
- @(snta_conv … (ⓓV2.U2)) /2 width=2/ /3 width=2/ (**) (* explicit constructor, /4 width=5/ is too slow *)
- | #V0 #V2 #W0 #W2 #T0 #T2 #_ #_ #_ #_ #H destruct
- ]
-*)
-| #L1 #V1 #T1 #U1 #W1 #l #_ #HUW1 #IHTU1 #_ #L2 #HL12 #X #H #Hl
- elim (tpr_inv_appl1 … H) -H *
- [ #V2 #T2 #HV12 #HT12 #H destruct
- lapply (cpr_tpr … HV12 L2) #HV
- elim (snta_fwd_correct h L2 (ⓐV1.T1) (ⓐV1.U1) (l+1) ?) [2: /3 width=6/ ] #U
- @(snta_conv … (ⓐV2.U1)) /2 width=1/ -HV12 /4 width=8 by snta_pure, cprs_flat_dx/ (**) (* explicit constructor, /4 width=8/ is too slow without trace *)
- | #V2 #W0 #T0 #T2 #HV12 #HT02 #H1 #H2 destruct
- lapply (IHTU1 … HL12 (ⓛW0.T2) ? ?) -IHTU1 // /2 width=1/ -T0 #H1
- lapply (IH … (ⓐV2.U1) … HUW1 HL12 ?) // /3 width=1/ #H2
- lapply (snta_pure … H1 H2) -H2 #H
- elim (snta_inv_bind1 … H1) -H1 #V0 #U2 #l1 #HWV0 #HTU2 #HU21
- @(snta_conv … (ⓓV2.U2)) (**) (* explicit constructor *)
- [2:
-(*
- @snta_bind /3 width=2/ /3 width=6/ (**) (* /4 width=6/ is a bit slow *)
-*)
- |3: @(cpcs_cpr_conf … (ⓐV1.ⓛW0.U2)) /2 width=1/
- |4: /2 width=5/
- | skip
- ]
-(*
- elim (snta_fwd_pure1 … H) -H #T1 #W2 #HVW2 #HUT1 #HTW1
-
- elim (cpcs_inv_abst1 … HU21) #W3 #U3 #HU13 #H
- elim (cprs_inv_abst … H Abst W0) -H #HW03 #_
- elim (pippo … IH … HUW1 ? V2 W3 U3 HL12 ? ?) -IH -HUW1 -HL12 // /3 width=1/ -HU13 #l2 #HV2W3
- lapply (snta_conv h L2 V2 W3 W0 V0 (l1+1) ? ? ?) /2 width=1/ -HV2W3 -HW03 -HWV0 #HV2W0
-*)
-(* SEGMENT 1.5
- lapply (IH … HV1 … HL12 … HV12) -HV1 -HV12 /width=5/ #HB
- lapply (IH … HB0 … HL12 W2 ?) -HB0 /width=5/ #HB0
- lapply (IH … HA0 … (L2.ⓛW2) … HT02) -IH -HA0 -HT02 /width=5/ -T0 /2 width=1/ -L1 -V1 /4 width=7/
-
-axiom pippo: ⦃h, L⦄ ⊢ ⓐV.X : Y →
- ∃∃W,T. L ⊢ X ➡* ⓛW.T & ⦃h, L⦄ ⊢ ⓐV : W.
-
-*)
-(* SEGMENT 2
-| #L1 #T1 #U1 #W1 #_ #_ #IHTU1 #IHUW1 #L2 #d #e #HL12 #X #H
- elim (tpss_inv_flat1 … H) -H #U2 #T2 #HU12 #HT12 #H destruct
- lapply (cpr_tpss … HU12) /4 width=4/
-| #L1 #T1 #U11 #U12 #U #_ #HU112 #_ #IHTU11 #IHU12 #L2 #d #e #HL12 #T2 #HT12
- @(snta_conv … U11) /2 width=5/ (**) (* explicot constructor, /3 width=7/ is too slow *)
-]
-qed.
-*)
-
-(* SEGMENT 3
-fact snta_ltpr_tpr_conf_aux: ∀h,L,T,L1,T1,U. ⦃h, L1⦄ ⊢ T1 : U → L = L1 → T = T1 →
- ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 : U.
-
-
- | #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HW02 #HT02 #HV02 #H1 #H2 destruct
- elim (snta_inv_abbr … HT1) -HT1 #B0 #HW0 #HT0
- lapply (IH … HW0 … HL12 … HW02) -HW0 /width=5/ #HW2
- lapply (IH … HV1 … HL12 … HV10) -HV1 -HV10 /width=5/ #HV0
- lapply (IH … HT0 … (L2.ⓓW2) … HT02) -IH -HT0 -HT02 /width=5/ -V1 -T0 /2 width=1/ -L1 -W0 #HT2
- @(snta_abbr … HW2) -HW2
- @(snta_appl … HT2) -HT2 /3 width=7/ (**) (* explict constructors, /5 width=7/ is too slow *)
- ]
-| #L1 #V1 #T1 #A #HV1 #HT1 #H1 #H2 #L2 #HL12 #X #H destruct
- elim (tpr_inv_cast1 … H) -H
- [ * #V2 #T2 #HV12 #HT12 #H destruct
- lapply (IH … HV1 … HL12 … HV12) -HV1 -HV12 /width=5/ #HV2
- lapply (IH … HT1 … HL12 … HT12) -IH -HT1 -HL12 -HT12 /width=5/ -L1 -V1 -T1 /2 width=1/
- | -HV1 #HT1X
- lapply (IH … HT1 … HL12 … HT1X) -IH -HT1 -HL12 -HT1X /width=5/
- ]
-]
-qed.
-
-lemma snta_ltpr_tpr_conf: ∀h,L1,T1,U. ⦃h, L1⦄ ⊢ T1 : U → ∀L2. L1 ➡ L2 →
- ∀T2. T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 : U.
-
-/2 width=9/ qed.
-
-axiom snta_ltpr_conf: ∀L1,T,A. L1 ⊢ T : A → ∀L2. L1 ➡ L2 → L2 ⊢ T : A.
-/2 width=5/ qed.
-
-axiom snta_tpr_conf: ∀L,T1,A. L ⊢ T1 : A → ∀T2. T1 ➡ T2 → L ⊢ T2 : A.
-/2 width=5/ qed.
-*)
-*)*)
\ No newline at end of file
projects / helm.git / blobdiff