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
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
@(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
@(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