Theorems · Theorem · real analysis

Monovary.sum_comp_perm_mul_eq_sum_mul_iff

∀ {ι : Type u_1} {α : Type u_2} [inst : Semiring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [ExistsAddOfLE α]
  {σ : Equiv.Perm ι} {f g : ι → α} [inst_4 : Fintype ι],
  Monovary f g → (∑ i, f (σ i) * g i = ∑ i, f i * g i ↔ Monovary (f ∘ ⇑σ) g)

Equality case of the Rearrangement Inequality: Pointwise multiplication of f and g, which monovary together, is unchanged by a permutation if and only if f ∘ σ and g monovary together. Stated by permuting the entries of g.

Defined in

Mathlib.Algebra.Order.Rearrangement

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringLinearOrderIsStrictOrderedRingExistsAddOfLEFintype