lemma cofrees_fwd_lift: āL,U,d,i. L ā¢ i ~Ļµ š
*[d]ā¦Uā¦ ā āT. ā§[i, 1] T ā” U.
/2 width=1 by/ qed-.
-lemma cofrees_fwd_nlift: āL,U,d,i. (āT. ā§[i, 1] T ā” U ā ā„) ā (L ā¢ i ~Ļµ š
*[d]ā¦Uā¦ ā ā„).
-#L #U #d #i #HnTU #H elim (cofrees_fwd_lift ā¦ H) -H /2 width=2 by/
-qed-.
-
lemma cofrees_fwd_bind_sn: āa,I,L,W,U,i,d. L ā¢ i ~Ļµ š
*[d]ā¦ā{a,I}W.Uā¦ ā
L ā¢ i ~Ļµ š
*[d]ā¦Wā¦.
#a #I #L #W1 #U #i #d #H #W2 #HW12 elim (H (ā{a,I}W2.U)) /2 width=1 by cpys_bind/ -W1