(* Basic properties *********************************************************)
+lemma tps_tpss: ∀L,T1,T2,d,e. L ⊢ T1 ▶ [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
+/2 width=1/ qed.
+
lemma tpss_strap1: ∀L,T1,T,T2,d,e.
- L ⊢ T1 ▶* [d, e] T → L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
+ L ⊢ T1 ▶* [d, e] T → L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
/2 width=3/ qed.
lemma tpss_strap2: ∀L,T1,T,T2,d,e.
- L ⊢ T1 ▶ [d, e] T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
+ L ⊢ T1 ▶ [d, e] T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
/2 width=3/ qed.
lemma tpss_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▶* [d, e] T2 →
qed-.
lemma tpss_inv_bind1: ∀d,e,L,a,I,V1,T1,U2. L ⊢ ⓑ{a,I} V1. T1 ▶* [d, e] U2 →
- ∃∃V2,T2. L ⊢ V1 ▶* [d, e] V2 &
+ ∃∃V2,T2. L ⊢ V1 ▶* [d, e] V2 &
L. ⓑ{I} V2 ⊢ T1 ▶* [d + 1, e] T2 &
U2 = ⓑ{a,I} V2. T2.
#d #e #L #a #I #V1 #T1 #U2 #H @(tpss_ind … H) -U2
(* Basic forward lemmas *****************************************************)
-lemma tpss_fwd_tw: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e] T2 → #{T1} ≤ #{T2}.
+lemma tpss_fwd_tw: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e] T2 → ♯{T1} ≤ ♯{T2}.
#L #T1 #T2 #d #e #H @(tpss_ind … H) -T2 //
#T #T2 #_ #HT2 #IHT1
lapply (tps_fwd_tw … HT2) -HT2 #HT2
elim (tps_fwd_shift1 … H0) -H0 #L2 #T2 #HL02 #H destruct /2 width=4/
]
qed-.
-
\ No newline at end of file