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Mathlib/Algebra/Order/Field/Canonical/Defs.lean

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@@ -16,8 +16,7 @@ import Mathlib.Algebra.Order.WithZero
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variable {α : Type _} [LinearOrderedSemifield α] [CanonicallyOrderedAdd α]
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-- See note [lower instance priority]
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instance (priority := 100) CanonicallyOrderedAdd.toLinearOrderedCommGroupWithZero :
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abbrev CanonicallyOrderedAdd.toLinearOrderedCommGroupWithZero :
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LinearOrderedCommGroupWithZero α :=
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{ ‹LinearOrderedSemifield α› with
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mul_le_mul_left := fun a b h c ↦ mul_le_mul_of_nonneg_left h <| zero_le _ }

Mathlib/Algebra/Order/Ring/Canonical.lean

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@@ -82,8 +82,7 @@ instance (priority := 100) toOrderedCommMonoid
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mul_le_mul_left _ _ := mul_le_mul_left'
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#align canonically_ordered_comm_semiring.to_ordered_comm_monoid CanonicallyOrderedAdd.toOrderedCommMonoid
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-- see Note [lower instance priority]
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instance (priority := 100) toOrderedCommSemiring
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abbrev toOrderedCommSemiring
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[CommSemiring α] [PartialOrder α] [CanonicallyOrderedAdd α]
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[CovariantClass α α (· + ·) (· ≤ ·)] :
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OrderedCommSemiring α where
@@ -93,7 +92,7 @@ instance (priority := 100) toOrderedCommSemiring
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mul_le_mul_of_nonneg_left := fun _ _ _ h _ => mul_le_mul_left' h _
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mul_le_mul_of_nonneg_right := fun _ _ _ h _ => mul_le_mul_right' h _
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#align canonically_ordered_comm_semiring.to_ordered_comm_semiring CanonicallyOrderedAdd.toOrderedCommSemiring
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--[OrderedSemiring α] [CanonicallyOrderedAdd α]
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@[simp]
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theorem mul_pos [NonUnitalNonAssocSemiring α] [PartialOrder α] [CanonicallyOrderedAdd α]
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[NoZeroDivisors α] {a b : α} :

Mathlib/Data/DFinsupp/Lex.lean

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@@ -194,7 +194,8 @@ section OrderedAddMonoid
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variable [LinearOrder ι]
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instance Lex.orderBot [∀ i, CanonicallyOrderedAddCommMonoid (α i)] :
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instance Lex.orderBot [∀ i, AddZeroClass (α i)] [∀ i, PartialOrder (α i)]
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[∀ i, CanonicallyOrderedAdd (α i)] :
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OrderBot (Lex (Π₀ i, α i)) where
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bot := 0
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bot_le _ := DFinsupp.toLex_monotone bot_le

Mathlib/RingTheory/MvPolynomial/Symmetric.lean

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@@ -303,7 +303,7 @@ theorem psum_one : psum σ R 1 = ∑ i, X i := by
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@[simp]
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theorem rename_psum (n : ℕ) (e : σ ≃ τ) : rename e (psum σ R n) = psum τ R n := by
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simp_rw [psum, map_sum, map_pow, rename_X, e.sum_comp (X · ^ n)]
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simp_rw [psum, map_sum, map_pow, rename_X, e.sum_comp (fun i ↦ (X i ^ n : MvPolynomial τ R))]
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theorem psum_isSymmetric (n : ℕ) : IsSymmetric (psum σ R n) := rename_psum _ _ n
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