eval_zero — Mathlib

English

Let f be a partial Hahn embedding under the stated order and Archimedean assumptions. Then the evaluation at zero vanishes: f.eval(0) = 0.

Русский

Пусть f — частичное Ган-встраивание при заданных условиях порядка и Архимеева. Тогда значение при 0 равно 0: f.eval(0) = 0.

LaTeX

$$$f(0)=0$$$

Lean4

@[simp]
theorem eval_zero [IsOrderedAddMonoid R] [Archimedean R] : f.eval 0 = 0 :=
  by
  unfold eval
  convert toLex_zero
  ext c
  rw [f.evalCoeff_eq (y := 0) (by simp)]
  simp

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