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chore(set_theory/ordinal/basic): remove rel_iso_out (#15145)
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This is just a specific application of `rel_iso.cast`. Moreover, it's unused.
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vihdzp committed Jul 7, 2022
1 parent 9b2755b commit bf735cd
Showing 1 changed file with 0 additions and 10 deletions.
10 changes: 0 additions & 10 deletions src/set_theory/ordinal/basic.lean
Expand Up @@ -590,16 +590,6 @@ begin
cases quotient.out α, cases quotient.out β, exact classical.choice
end

/-- Given two ordinals `α = β`, then `rel_iso_out α β` is the order isomorphism between two
model types for `α` and `β`. -/
def rel_iso_out {α β : ordinal} (h : α = β) :
((<) : α.out.α → α.out.α → Prop) ≃r ((<) : β.out.α → β.out.α → Prop) :=
begin
change α.out.r ≃r β.out.r,
rw [←quotient.out_eq α, ←quotient.out_eq β] at h, revert h,
cases quotient.out α, cases quotient.out β, exact classical.choice ∘ quotient.exact
end

theorem typein_lt_type (r : α → α → Prop) [is_well_order α r] (a : α) : typein r a < type r :=
⟨principal_seg.of_element _ _⟩

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