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feat(CategoryTheory/ChosenFiniteProducts.lean): simp lemmas for lef…
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…t and right unitors in `ChosenFiniteProducts` monoidal structure (#17695)

Add 4 `simp` lemmas for left and right unitors in the monoidal structure obtained from instances of `ChosenFiniteProducts`.
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Robin Carlier committed Oct 13, 2024
1 parent 9d6891a commit 6a98dbd
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16 changes: 16 additions & 0 deletions Mathlib/CategoryTheory/ChosenFiniteProducts.lean
Original file line number Diff line number Diff line change
Expand Up @@ -178,6 +178,22 @@ lemma associator_inv_fst_snd (X Y Z : C) :
lemma associator_inv_snd (X Y Z : C) :
(α_ X Y Z).inv ≫ snd _ _ = snd _ _ ≫ snd _ _ := lift_snd _ _

@[reassoc (attr := simp)]
lemma leftUnitor_inv_fst (X : C) :
(λ_ X).inv ≫ fst _ _ = toUnit _ := toUnit_unique _ _

@[reassoc (attr := simp)]
lemma leftUnitor_inv_snd (X : C) :
(λ_ X).inv ≫ snd _ _ = 𝟙 X := lift_snd _ _

@[reassoc (attr := simp)]
lemma rightUnitor_inv_fst (X : C) :
(ρ_ X).inv ≫ fst _ _ = 𝟙 X := lift_fst _ _

@[reassoc (attr := simp)]
lemma rightUnitor_inv_snd (X : C) :
(ρ_ X).inv ≫ snd _ _ = toUnit _ := toUnit_unique _ _

/--
Construct an instance of `ChosenFiniteProducts C` given an instance of `HasFiniteProducts C`.
-/
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