(* LABELLED TRANSITIVE CLOSURE **********************************************)
-alias symbol "subseteq" = "relation inclusion".
+alias symbol "subseteq" = "relation inclusion". (**)
-(* Properties with contextual transitive closure ****************************)
+(* Constructions with contextual transitive closure *************************)
lemma ltc_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
left_identity … f i →
#b #b2 #_ #Hb2 #IH >(Hf i) -Hf /2 width=3 by ltc_dx/
qed.
-(* Inversion lemmas with contextual transitive closure **********************)
+(* Inversions with contextual transitive closure ****************************)
lemma ltc_inv_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
associative … f → annulment_2 … f i →
∀c. ltc … f … (R c) i ⊆ CTC … (λc. R c i) c.
#C #A #i #f #B #R #H1f #H2f #c #b1 #b2
-@(insert_eq_0 … i) #a #H
+@(insert_eq_1 … i) #a #H
@(ltc_ind_dx A f B … H) -a -b2 /2 width=1 by inj/ -H1f
#a1 #a2 #b #b2 #_ #IH #Hb2 #H <H
elim (H2f … H) -H2f -H #H1 #H2 destruct