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[Merged by Bors] - chore(Logic/Equiv): change type of sumEquivSigmaBool to simp normal form #21338

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[Merged by Bors] - chore(Logic/Equiv): change type of sumEquivSigmaBool to simp normal form #21338

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931dae0
chore(Logic/Equiv): replace `Bool.casesOn` with `Bool.rec` in `sumEqu…
lambda-fairy Feb 2, 2025
1ffe26d
Use `bif` instead
lambda-fairy Feb 2, 2025
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4 changes: 2 additions & 2 deletions Mathlib/Logic/Equiv/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ In this file we continue the work on equivalences begun in `Mathlib/Logic/Equiv/
* canonical isomorphisms between various types: e.g.,

- `Equiv.sumEquivSigmaBool` is the canonical equivalence between the sum of two types `α ⊕ β`
and the sigma-type `Σ b : Bool, b.casesOn α β`;
and the sigma-type `Σ b, bif b then β else α`;

- `Equiv.prodSumDistrib : α × (β ⊕ γ) ≃ (α × β) ⊕ (α × γ)` shows that type product and type sum
satisfy the distributive law up to a canonical equivalence;
Expand Down Expand Up @@ -476,7 +476,7 @@ def piOptionEquivProd {α} {β : Option α → Type*} :
`β` to be types from the same universe, so it cannot be used directly to transfer theorems about
sigma types to theorems about sum types. In many cases one can use `ULift` to work around this
difficulty. -/
def sumEquivSigmaBool (α β) : α ⊕ β ≃ Σ b : Bool, b.casesOn α β :=
def sumEquivSigmaBool (α β) : α ⊕ β ≃ Σ b, bif b then β else α :=
⟨fun s => s.elim (fun x => ⟨false, x⟩) fun x => ⟨true, x⟩, fun s =>
match s with
| ⟨false, a⟩ => inl a
Expand Down
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