(* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
-(* Advanced forward lemmas on context-sensitive irreducible terms ***********)
+(* Advanced forward lemmas on irreducibility ********************************)
lemma cpr_fwd_cir: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T1⦄ → T2 = T1.
#G #L #T1 #T2 #H elim H -G -L -T1 -T2
| #G #L #V1 #T1 #T #T2 #_ #_ #_ #H
elim (cir_inv_ri2 … H) /2 width=1 by or_introl/
| #G #L #V1 #T1 #T2 #_ #_ #H
- elim (cir_inv_ri2 … H) /2 width=1/
+ elim (cir_inv_ri2 … H) /2 width=1 by/
| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #H
elim (cir_inv_appl … H) -H #_ #_ #H
elim (simple_inv_bind … H)