weight_single_one_apply — Mathlib

English

If you take the weight of the singleton s with unit weight, weight w (Pi.single s 1) equals w(s) and equals the value of f at s when f = Pi.single s 1.

Русский

Вес единичной одиночки равен весу на этот индекс: weight w (Pi.single s 1) = w(s).

LaTeX

$$weight w (Finsupp.single s 1) = w s$$

Lean4

theorem weight_single_one_apply [DecidableEq σ] (s : σ) (f : σ →₀ R) : weight (Pi.single s 1) f = f s := by
  rw [weight_single_index, smul_eq_mul, mul_one]

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