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feat(topology/continuous_map): missing coe_mk lemma (#6087)
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Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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semorrison and semorrison committed Feb 8, 2021
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3 changes: 3 additions & 0 deletions src/topology/continuous_map.lean
Expand Up @@ -46,6 +46,9 @@ instance [inhabited β] : inhabited C(α, β) :=
lemma coe_inj ⦃f g : C(α, β)⦄ (h : (f : α → β) = g) : f = g :=
by cases f; cases g; cases h; refl

@[simp] lemma coe_mk (f : α → β) (h : continuous f) :
⇑(⟨f, h⟩ : continuous_map α β) = f := rfl

/-- The identity as a continuous map. -/
def id : C(α, α) := ⟨id⟩

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