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fix(data/equiv/basic): use subtype p not coe_sort (set_of p) (#9559)
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`↥{x | p x}` is just a clumsy way to write `{x // p x}`.
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eric-wieser committed Oct 5, 2021
1 parent da4d550 commit 5926f10
Showing 1 changed file with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion src/data/equiv/basic.lean
Expand Up @@ -1446,7 +1446,7 @@ end
/-- The `pi`-type `Π i, π i` is equivalent to the type of sections `f : ι → Σ i, π i` of the
`sigma` type such that for all `i` we have `(f i).fst = i`. -/
def pi_equiv_subtype_sigma (ι : Type*) (π : ι → Type*) :
(Πi, π i) ≃ {f : ι → Σi, π i | ∀i, (f i).1 = i } :=
(Π i, π i) ≃ {f : ι → Σ i, π i // ∀ i, (f i).1 = i } :=
⟨ λf, ⟨λi, ⟨i, f i⟩, assume i, rfl⟩, λf i, begin rw ← f.2 i, exact (f.1 i).2 end,
assume f, funext $ assume i, rfl,
assume ⟨f, hf⟩, subtype.eq $ funext $ assume i, sigma.eq (hf i).symm $
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