/2 width=1/ qed.
lemma tpss_bind: ∀L,V1,V2,d,e. L ⊢ V1 [d, e] ▶* V2 →
- ∀I,T1,T2. L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ▶* T2 →
- L ⊢ 𝕓{I} V1. T1 [d, e] ▶* 𝕓{I} V2. T2.
+ ∀I,T1,T2. L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶* T2 →
+ L ⊢ ⓑ{I} V1. T1 [d, e] ▶* ⓑ{I} V2. T2.
#L #V1 #V2 #d #e #HV12 elim HV12 -V2
[ #V2 #HV12 #I #T1 #T2 #HT12 elim HT12 -T2
[ /3 width=5/
| #T #T2 #_ #HT2 #IHT @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
]
| #V #V2 #_ #HV12 #IHV #I #T1 #T2 #HT12
- lapply (tpss_lsubs_conf … HT12 (L. 𝕓{I} V) ?) -HT12 /2 width=1/ #HT12
+ lapply (tpss_lsubs_conf … HT12 (L. ⓑ{I} V) ?) -HT12 /2 width=1/ #HT12
lapply (IHV … HT12) -IHV -HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
]
qed.
lemma tpss_flat: ∀L,I,V1,V2,T1,T2,d,e.
L ⊢ V1 [d, e] ▶ * V2 → L ⊢ T1 [d, e] ▶* T2 →
- L ⊢ 𝕗{I} V1. T1 [d, e] ▶* 𝕗{I} V2. T2.
+ L ⊢ ⓕ{I} V1. T1 [d, e] ▶* ⓕ{I} V2. T2.
#L #I #V1 #V2 #T1 #T2 #d #e #HV12 elim HV12 -V2
[ #V2 #HV12 #HT12 elim HT12 -T2
[ /3 width=1/
]
qed-.
-lemma tpss_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕓{I} V1. T1 [d, e] ▶* U2 →
+lemma tpss_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓑ{I} V1. T1 [d, e] ▶* U2 →
∃∃V2,T2. L ⊢ V1 [d, e] ▶* V2 &
- L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ▶* T2 &
- U2 = 𝕓{I} V2. T2.
+ L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶* T2 &
+ U2 = ⓑ{I} V2. T2.
#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -U2
[ /2 width=5/
| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
elim (tps_inv_bind1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H
- lapply (tpss_lsubs_conf … HT1 (L. 𝕓{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
+ lapply (tpss_lsubs_conf … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
]
qed-.
-lemma tpss_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕗{I} V1. T1 [d, e] ▶* U2 →
+lemma tpss_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓕ{I} V1. T1 [d, e] ▶* U2 →
∃∃V2,T2. L ⊢ V1 [d, e] ▶* V2 & L ⊢ T1 [d, e] ▶* T2 &
- U2 = 𝕗{I} V2. T2.
+ U2 = ⓕ{I} V2. T2.
#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -U2
[ /2 width=5/
| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct