(* *)
(**************************************************************************)
-include "basic_2/notation/relations/predsn_4.ma".
-include "basic_2/relocation/lex.ma".
+include "basic_2/notation/relations/predsn_5.ma".
+include "static_2/relocation/lex.ma".
include "basic_2/rt_transition/cpr_ext.ma".
(* PARALLEL R-TRANSITION FOR FULL LOCAL ENVIRONMENTS ************************)
-definition lpr (h) (G): relation lenv ≝
- lex (λL. cpm h G L 0).
+definition lpr (h) (n) (G): relation lenv ≝
+ lex (λL. cpm h G L n).
interpretation
"parallel rt-transition (full local environment)"
- 'PRedSn h G L1 L2 = (lpr h G L1 L2).
+ 'PRedSn h n G L1 L2 = (lpr h n G L1 L2).
(* Basic properties *********************************************************)
-lemma lpr_bind (h) (G): â\88\80K1,K2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 →
- â\88\80I1,I2. â¦\83G, K1â¦\84 â\8a¢ I1 â\9e¡[h] I2 â\86\92 â¦\83G, K1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h] K2.â\93\98{I2}.
+lemma lpr_bind (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 →
+ â\88\80I1,I2. â\9dªG,K1â\9d« â\8a¢ I1 â\9e¡[h,0] I2 â\86\92 â\9dªG,K1.â\93\98[I1]â\9d« â\8a¢ â\9e¡[h,0] K2.â\93\98[I2].
/2 width=1 by lex_bind/ qed.
(* Note: lemma 250 *)
-lemma lpr_refl (h) (G): reflexive … (lpr h G).
+lemma lpr_refl (h) (G): reflexive … (lpr h 0 G).
/2 width=1 by lex_refl/ qed.
(* Advanced properties ******************************************************)
-lemma lpr_bind_refl_dx (h) (G): â\88\80K1,K2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 →
- â\88\80I. â¦\83G, K1.â\93\98{I}â¦\84 â\8a¢ â\9e¡[h] K2.â\93\98{I}.
+lemma lpr_bind_refl_dx (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 →
+ â\88\80I. â\9dªG,K1.â\93\98[I]â\9d« â\8a¢ â\9e¡[h,0] K2.â\93\98[I].
/2 width=1 by lex_bind_refl_dx/ qed.
-lemma lpr_pair (h) (G): â\88\80K1,K2,V1,V2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 â\86\92 â¦\83G, K1â¦\84 â\8a¢ V1 â\9e¡[h] V2 →
- â\88\80I. â¦\83G, K1.â\93\91{I}V1â¦\84 â\8a¢ â\9e¡[h] K2.â\93\91{I}V2.
+lemma lpr_pair (h) (G): â\88\80K1,K2,V1,V2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 â\86\92 â\9dªG,K1â\9d« â\8a¢ V1 â\9e¡[h,0] V2 →
+ â\88\80I. â\9dªG,K1.â\93\91[I]V1â\9d« â\8a¢ â\9e¡[h,0] K2.â\93\91[I]V2.
/2 width=1 by lex_pair/ qed.
(* Basic inversion lemmas ***************************************************)
(* Basic_2A1: was: lpr_inv_atom1 *)
(* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom_sn (h) (G): â\88\80L2. â¦\83G, â\8b\86â¦\84 â\8a¢ â\9e¡[h] L2 → L2 = ⋆.
+lemma lpr_inv_atom_sn (h) (G): â\88\80L2. â\9dªG,â\8b\86â\9d« â\8a¢ â\9e¡[h,0] L2 → L2 = ⋆.
/2 width=2 by lex_inv_atom_sn/ qed-.
-lemma lpr_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â¦\83G, K1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83I2,K2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & â¦\83G, K1â¦\84 â\8a¢ I1 â\9e¡[h] I2 &
- L2 = K2.ⓘ{I2}.
+lemma lpr_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â\9dªG,K1.â\93\98[I1]â\9d« â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83I2,K2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« â\8a¢ I1 â\9e¡[h,0] I2 &
+ L2 = K2.ⓘ[I2].
/2 width=1 by lex_inv_bind_sn/ qed-.
(* Basic_2A1: was: lpr_inv_atom2 *)
-lemma lpr_inv_atom_dx (h) (G): â\88\80L1. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] ⋆ → L1 = ⋆.
+lemma lpr_inv_atom_dx (h) (G): â\88\80L1. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] ⋆ → L1 = ⋆.
/2 width=2 by lex_inv_atom_dx/ qed-.
-lemma lpr_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] K2.â\93\98{I2} →
- â\88\83â\88\83I1,K1. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & â¦\83G, K1â¦\84 â\8a¢ I1 â\9e¡[h] I2 &
- L1 = K1.ⓘ{I1}.
+lemma lpr_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] K2.â\93\98[I2] →
+ â\88\83â\88\83I1,K1. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« â\8a¢ I1 â\9e¡[h,0] I2 &
+ L1 = K1.ⓘ[I1].
/2 width=1 by lex_inv_bind_dx/ qed-.
(* Advanced inversion lemmas ************************************************)
-lemma lpr_inv_unit_sn (h) (G): â\88\80I,L2,K1. â¦\83G, K1.â\93¤{I}â¦\84 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83K2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & L2 = K2.â\93¤{I}.
+lemma lpr_inv_unit_sn (h) (G): â\88\80I,L2,K1. â\9dªG,K1.â\93¤[I]â\9d« â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83K2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & L2 = K2.â\93¤[I].
/2 width=1 by lex_inv_unit_sn/ qed-.
(* Basic_2A1: was: lpr_inv_pair1 *)
(* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â¦\83G, K1.â\93\91{I}V1â¦\84 â\8a¢ â\9e¡[h] L2 →
- â\88\83â\88\83K2,V2. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & â¦\83G, K1â¦\84 â\8a¢ V1 â\9e¡[h] V2 &
- L2 = K2.ⓑ{I}V2.
+lemma lpr_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â\9dªG,K1.â\93\91[I]V1â\9d« â\8a¢ â\9e¡[h,0] L2 →
+ â\88\83â\88\83K2,V2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« â\8a¢ V1 â\9e¡[h,0] V2 &
+ L2 = K2.ⓑ[I]V2.
/2 width=1 by lex_inv_pair_sn/ qed-.
-lemma lpr_inv_unit_dx (h) (G): â\88\80I,L1,K2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] K2.â\93¤{I} →
- â\88\83â\88\83K1. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & L1 = K1.â\93¤{I}.
+lemma lpr_inv_unit_dx (h) (G): â\88\80I,L1,K2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] K2.â\93¤[I] →
+ â\88\83â\88\83K1. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & L1 = K1.â\93¤[I].
/2 width=1 by lex_inv_unit_dx/ qed-.
(* Basic_2A1: was: lpr_inv_pair2 *)
-lemma lpr_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] K2.â\93\91{I}V2 →
- â\88\83â\88\83K1,V1. â¦\83G, K1â¦\84 â\8a¢ â\9e¡[h] K2 & â¦\83G, K1â¦\84 â\8a¢ V1 â\9e¡[h] V2 &
- L1 = K1.ⓑ{I}V1.
+lemma lpr_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] K2.â\93\91[I]V2 →
+ â\88\83â\88\83K1,V1. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« â\8a¢ V1 â\9e¡[h,0] V2 &
+ L1 = K1.ⓑ[I]V1.
/2 width=1 by lex_inv_pair_dx/ qed-.
-lemma lpr_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â¦\83G, L1.â\93\91{I1}V1â¦\84 â\8a¢ â\9e¡[h] L2.â\93\91{I2}V2 →
- â\88§â\88§ â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] L2 & â¦\83G, L1â¦\84 â\8a¢ V1 â\9e¡[h] V2 & I1 = I2.
+lemma lpr_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â\9dªG,L1.â\93\91[I1]V1â\9d« â\8a¢ â\9e¡[h,0] L2.â\93\91[I2]V2 →
+ â\88§â\88§ â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] L2 & â\9dªG,L1â\9d« â\8a¢ V1 â\9e¡[h,0] V2 & I1 = I2.
/2 width=1 by lex_inv_pair/ qed-.
(* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
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