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chore(set_theory/ordinal/basic): golf ordinal addition definition (#1…
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vihdzp committed Jun 15, 2022
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Showing 1 changed file with 1 addition and 2 deletions.
3 changes: 1 addition & 2 deletions src/set_theory/ordinal/basic.lean
Expand Up @@ -944,8 +944,7 @@ the addition, together with properties of the other operations, are proved in
every element of `o₁` is smaller than every element of `o₂`. -/
instance : has_add ordinal.{u} :=
⟨λ o₁ o₂, quotient.lift_on₂ o₁ o₂
(λ ⟨α, r, wo⟩ ⟨β, s, wo'⟩, ⟦⟨α ⊕ β, sum.lex r s, by exactI sum.lex.is_well_order _ _⟩⟧
: Well_order → Well_order → ordinal) $
(λ ⟨α, r, wo⟩ ⟨β, s, wo'⟩, by exactI type (sum.lex r s)) $
λ ⟨α₁, r₁, o₁⟩ ⟨α₂, r₂, o₂⟩ ⟨β₁, s₁, p₁⟩ ⟨β₂, s₂, p₂⟩ ⟨f⟩ ⟨g⟩,
quot.sound ⟨rel_iso.sum_lex_congr f g⟩⟩

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