English
A simplification lemma giving an equality relating equivSucc to a canonical embedding equality at a successor.
Русский
Упростяющее лемма, связывающая equivSucc с каноническим вложением на переходе к successor.
LaTeX
$$$$EquivSucc_i = \\text{canonical embedding equality at } i+1$$$$
Lean4
/-- Extend the family `E⟮<i⟯, i : ι` by adjoining a top element. -/
@[simps!]
def filtration : WithTop ι ↪o IntermediateField F E :=
.ofStrictMono (fun i ↦ i.recTopCoe ⊤ (E⟮<·⟯)) fun i j h ↦
by
cases j
· obtain ⟨i, rfl⟩ := ne_top_iff_exists.mp h.ne
exact ⟨le_top, fun incl ↦ (isLeast_leastExt i).1 (incl trivial)⟩
· obtain ⟨i, rfl⟩ := ne_top_iff_exists.mp (h.trans <| coe_lt_top _).ne
exact strictMono_filtration (coe_lt_coe.mp h)
