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Change coe_singleton type to explicitly convert Set -> _root_.Set #436

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teorth merged 2 commits into from
Jan 29, 2026
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Change coe_singleton type to explicitly convert Set -> _root_.Set #436

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b14fdf2
Change coe_singleton type to explicitly convert Set -> _root_.Set
Shaunticlair Jan 27, 2026
5f9eb68
Update addition set coercion theorems with explicit typecasting
Shaunticlair Jan 29, 2026
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10 changes: 5 additions & 5 deletions analysis/Analysis/Section_3_1.lean
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Expand Up @@ -855,25 +855,25 @@ theorem SetTheory.Set.coe_ssubset (X Y:Set) :
(X : _root_.Set Object) ⊂ (Y : _root_.Set Object) ↔ X ⊂ Y := by sorry

/-- Compatibility of singleton -/
theorem SetTheory.Set.coe_singleton (x: Object) : ({x} : _root_.Set Object) = {x} := by sorry
theorem SetTheory.Set.coe_singleton (x: Object) : (({x}:Set) : _root_.Set Object) = {x} := by sorry

/-- Compatibility of union -/
theorem SetTheory.Set.coe_union (X Y: Set) :
(X ∪ Y : _root_.Set Object) = (X : _root_.Set Object) ∪ (Y : _root_.Set Object) := by sorry
((X ∪ Y:Set) : _root_.Set Object) = (X : _root_.Set Object) ∪ (Y : _root_.Set Object) := by sorry

/-- Compatibility of pair -/
theorem SetTheory.Set.coe_pair (x y: Object) : ({x, y} : _root_.Set Object) = {x, y} := by sorry
theorem SetTheory.Set.coe_pair (x y: Object) : (({x, y}:Set) : _root_.Set Object) = {x, y} := by sorry

/-- Compatibility of subtype -/
theorem SetTheory.Set.coe_subtype (X: Set) : (X : _root_.Set Object) = X.toSubtype := by sorry

/-- Compatibility of intersection -/
theorem SetTheory.Set.coe_intersection (X Y: Set) :
(X ∩ Y : _root_.Set Object) = (X : _root_.Set Object) ∩ (Y : _root_.Set Object) := by sorry
((X ∩ Y:Set) : _root_.Set Object) = (X : _root_.Set Object) ∩ (Y : _root_.Set Object) := by sorry

/-- Compatibility of set difference-/
theorem SetTheory.Set.coe_diff (X Y: Set) :
(X \ Y : _root_.Set Object) = (X : _root_.Set Object) \ (Y : _root_.Set Object) := by sorry
((X \ Y:Set) : _root_.Set Object) = (X : _root_.Set Object) \ (Y : _root_.Set Object) := by sorry

/-- Compatibility of disjointness -/
theorem SetTheory.Set.coe_Disjoint (X Y: Set) :
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