-lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
- ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → ≥[h] 𝐒❪G2,L2,T2❫.
+lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+ ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → ≥𝐒[h] ❪G2,L2,T2❫.
#h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
#G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
elim (fpbs_inv_fpbg … H12) -H12
#h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
#G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
elim (fpbs_inv_fpbg … H12) -H12
(* Properties with proper parallel rst-computation for closures *************)
lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
(* Properties with proper parallel rst-computation for closures *************)
lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
- ∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → ≥[h] 𝐒❪G2,L2,T2❫
- ) → ≥[h] 𝐒❪G1,L1,T1❫.
+ ∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → ≥𝐒[h] ❪G2,L2,T2❫
+ ) → ≥𝐒[h] ❪G1,L1,T1❫.
/4 width=1 by fsb_intro, fpb_fpbg/ qed.
(* Eliminators with proper parallel rst-computation for closures ************)
lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
/4 width=1 by fsb_intro, fpb_fpbg/ qed.
(* Eliminators with proper parallel rst-computation for closures ************)
lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
- (∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+ (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
(∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
Q G1 L1 T1
) →
(∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
Q G1 L1 T1
) →
- ∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+ ∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → Q G2 L2 T2.
#h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
#G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → Q G2 L2 T2.
#h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
#G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
- (∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+ (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
(∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
Q G1 L1 T1
) →
(∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
Q G1 L1 T1
) →
- ∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ → Q G1 L1 T1.
+ ∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ → Q G1 L1 T1.
(* Inversion lemmas with proper parallel rst-computation for closures *******)
lemma fsb_fpbg_refl_false (h) (G) (L) (T):
(* Inversion lemmas with proper parallel rst-computation for closures *******)
lemma fsb_fpbg_refl_false (h) (G) (L) (T):
- ≥[h] 𝐒❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.
+ ≥𝐒[h] ❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.