@@ -271,17 +271,16 @@ This is the `OneHom` version of `Pi.mulSingle`. -/
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as functions supported at a point.
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This is the `ZeroHom` version of `Pi.single`." ]
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- def OneHom.single [∀ i, One <| f i] (i : I) : OneHom (f i) (∀ i, f i) where
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+ nonrec def OneHom.mulSingle [∀ i, One <| f i] (i : I) : OneHom (f i) (∀ i, f i) where
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toFun := mulSingle i
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map_one' := mulSingle_one i
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- #align one_hom.single OneHom.single
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+ #align one_hom.single OneHom.mulSingle
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#align zero_hom.single ZeroHom.single
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@[to_additive (attr := simp)]
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- theorem OneHom.single_apply [∀ i, One <| f i] (i : I) (x : f i) :
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- OneHom.single f i x = mulSingle i x :=
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- rfl
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- #align one_hom.single_apply OneHom.single_apply
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+ theorem OneHom.mulSingle_apply [∀ i, One <| f i] (i : I) (x : f i) :
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+ mulSingle f i x = Pi.mulSingle i x := rfl
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+ #align one_hom.single_apply OneHom.mulSingle_apply
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#align zero_hom.single_apply ZeroHom.single_apply
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/-- The monoid homomorphism including a single monoid into a dependent family of additive monoids,
@@ -293,16 +292,16 @@ This is the `MonoidHom` version of `Pi.mulSingle`. -/
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of additive monoids, as functions supported at a point.
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This is the `AddMonoidHom` version of `Pi.single`." ]
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- def MonoidHom.single [∀ i, MulOneClass <| f i] (i : I) : f i →* ∀ i, f i :=
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- { OneHom.single f i with map_mul' := mulSingle_op₂ (fun _ => (· * ·)) (fun _ => one_mul _) _ }
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- #align monoid_hom.single MonoidHom.single
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+ def MonoidHom.mulSingle [∀ i, MulOneClass <| f i] (i : I) : f i →* ∀ i, f i :=
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+ { OneHom.mulSingle f i with map_mul' := mulSingle_op₂ (fun _ => (· * ·)) (fun _ => one_mul _) _ }
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+ #align monoid_hom.single MonoidHom.mulSingle
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#align add_monoid_hom.single AddMonoidHom.single
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@[to_additive (attr := simp)]
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- theorem MonoidHom.single_apply [∀ i, MulOneClass <| f i] (i : I) (x : f i) :
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- MonoidHom.single f i x = mulSingle i x :=
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+ theorem MonoidHom.mulSingle_apply [∀ i, MulOneClass <| f i] (i : I) (x : f i) :
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+ mulSingle f i x = Pi. mulSingle i x :=
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rfl
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- #align monoid_hom.single_apply MonoidHom.single_apply
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+ #align monoid_hom.single_apply MonoidHom.mulSingle_apply
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#align add_monoid_hom.single_apply AddMonoidHom.single_apply
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/-- The multiplicative homomorphism including a single `MulZeroClass`
@@ -335,22 +334,22 @@ theorem Pi.mulSingle_inf [∀ i, SemilatticeInf (f i)] [∀ i, One (f i)] (i : I
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@[to_additive]
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theorem Pi.mulSingle_mul [∀ i, MulOneClass <| f i] (i : I) (x y : f i) :
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mulSingle i (x * y) = mulSingle i x * mulSingle i y :=
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- (MonoidHom.single f i).map_mul x y
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+ (MonoidHom.mulSingle f i).map_mul x y
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#align pi.mul_single_mul Pi.mulSingle_mul
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#align pi.single_add Pi.single_add
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@[to_additive]
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theorem Pi.mulSingle_inv [∀ i, Group <| f i] (i : I) (x : f i) :
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mulSingle i x⁻¹ = (mulSingle i x)⁻¹ :=
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- (MonoidHom.single f i).map_inv x
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+ (MonoidHom.mulSingle f i).map_inv x
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#align pi.mul_single_inv Pi.mulSingle_inv
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#align pi.single_neg Pi.single_neg
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@[to_additive]
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- theorem Pi.single_div [∀ i, Group <| f i] (i : I) (x y : f i) :
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+ theorem Pi.mulSingle_div [∀ i, Group <| f i] (i : I) (x y : f i) :
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mulSingle i (x / y) = mulSingle i x / mulSingle i y :=
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- (MonoidHom.single f i).map_div x y
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- #align pi.single_div Pi.single_div
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+ (MonoidHom.mulSingle f i).map_div x y
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+ #align pi.single_div Pi.mulSingle_div
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#align pi.single_sub Pi.single_sub
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theorem Pi.single_mul [∀ i, MulZeroClass <| f i] (i : I) (x y : f i) :
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