copy — Mathlib

English

Copying a preordering along a new carrier S yields a preordering whose carrier is exactly S. The operations are inherited from the original structure but now live on S.

Русский

Копирование предпорядка по новому носителю S образует предпорядок с носителем ровно S; операции наследуются от исходной структуры и задаются на S.

LaTeX

$$$\\text{Copy of a preordering: } \\text{carrier}(P.copy(S,h_S)) = S$,$$

Lean4

/-- Copy of a preordering with a new `carrier` equal to the old one. Useful to fix definitional
equalities. -/
@[simps]
protected def copy : RingPreordering R where
  carrier := S
  zero_mem' := by aesop
  add_mem' ha hb := by aesop
  one_mem' := by aesop
  mul_mem' ha hb := by aesop

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