have ⟨c, ⟨m, hm⟩⟩ := s.split'
α : Type
inst✝ : Hierarchical α
rtr : α
cpt : Component
o : Component.type α cpt
i : ID
ho :
  rtr[cpt][match cpt with
      | Component.rtr => ↑i
      | Component.rcn => i
      | Component.val v => i] =
    some o
s : StrictMember cpt i rtr
hs : StrictMember.object s = o
⊢ ∃ c con, rtr[Component.rtr][c] = some con ∧ con{cpt}{i} = some o
α : Type
inst✝ : Hierarchical α
rtr : α
cpt : Component
o : Component.type α cpt
i : ID
ho :
  rtr[cpt][match cpt with
      | Component.rtr => ↑i
      | Component.rcn => i
      | Component.val v => i] =
    some o
s : StrictMember cpt i rtr
hs : StrictMember.object s = o
c : WithTop ID
m : Member Component.rtr c rtr
hm : Member.object m{cpt}{i} = some (StrictMember.object s)
⊢ ∃ c con, rtr[Component.rtr][c] = some con ∧ con{cpt}{i} = some o