(* Properties with application **********************************************)
lemma drops_tls_at: ∀f,i1,i2. @❪i1,f❫ ≘ i2 →
- â\88\80b,L1,L2. â\87©*[b,⫱*[i2]f] L1 ≘ L2 →
- â\87©*[b,⫯⫱*[↑i2]f] L1 ≘ L2.
+ â\88\80b,L1,L2. â\87©*[b,â«°*[i2]f] L1 ≘ L2 →
+ â\87©*[b,⫯⫰*[↑i2]f] L1 ≘ L2.
/3 width=3 by drops_eq_repl_fwd, at_inv_tls/ qed-.
lemma drops_split_trans_bind2: ∀b,f,I,L,K0. ⇩*[b,f] L ≘ K0.ⓘ[I] → ∀i. @❪O,f❫ ≘ i →
- â\88\83â\88\83J,K. â\87©[i]L â\89\98 K.â\93\98[J] & â\87©*[b,⫱*[â\86\91i]f] K â\89\98 K0 & â\87§*[⫱*[↑i]f] I ≘ J.
+ â\88\83â\88\83J,K. â\87©[i]L â\89\98 K.â\93\98[J] & â\87©*[b,â«°*[â\86\91i]f] K â\89\98 K0 & â\87§*[â«°*[↑i]f] I ≘ J.
#b #f #I #L #K0 #H #i #Hf
elim (drops_split_trans … H) -H [ |5: @(after_uni_dx … Hf) |2,3: skip ] /2 width=1 by after_isid_dx/ #Y #HLY #H
lapply (drops_tls_at … Hf … H) -H #H