-(* PARTIAL SUBSTITUTION ON TERMS ********************************************)
-
-(* Advanced inversion lemmas ************************************************)
-
-fact tps_inv_S2_aux: ∀L,T1,T2,d,e1. L ⊢ T1 ▶ [d, e1] T2 → ∀e2. e1 = e2 + 1 →
- ∀K,V. ⇩[0, d] L ≡ K. ⓛV → L ⊢ T1 ▶ [d + 1, e2] T2.
-#L #T1 #T2 #d #e1 #H elim H -L -T1 -T2 -d -e1
-[ //
-| #L #K0 #V0 #W #i #d #e1 #Hdi #Hide1 #HLK0 #HV0 #e2 #He12 #K #V #HLK destruct
- elim (lt_or_ge i (d+1)) #HiSd
- [ -Hide1 -HV0
- lapply (le_to_le_to_eq … Hdi ?) /2 width=1/ #H destruct
- lapply (ldrop_mono … HLK0 … HLK) #H destruct
- | -V -Hdi /2 width=4/
- ]
-| /4 width=3/
-| /3 width=3/
-]
-qed.
-
-lemma tps_inv_S2: ∀L,T1,T2,d,e. L ⊢ T1 ▶ [d, e + 1] T2 →
- ∀K,V. ⇩[0, d] L ≡ K. ⓛV → L ⊢ T1 ▶ [d + 1, e] T2.
-/2 width=3/ qed-.
-
-lemma tps_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 ▶ [d, 1] T2 →
- ∀K,V. ⇩[0, d] L ≡ K. ⓛV → T1 = T2.
-#L #T1 #T2 #d #HT12 #K #V #HLK
-lapply (tps_inv_S2 … T1 T2 … 0 … HLK) -K // -HT12 #HT12
-lapply (tps_inv_refl_O2 … HT12) -HT12 //
-qed-.