instField — Mathlib

English

Under appropriate domain conditions, RatFunc becomes a field with an embedding that respects field operations and passes through fractions.

Русский

При подходящих условиях область RatFunc образует поле с вложением, сохраняющим операции поля и дроби.

LaTeX

$$$\\text{RatFunc } K \\text{ carries a field structure with consistent algebra }$$

Lean4

@[stacks 09FK]
instance instField [IsDomain K] : Field (RatFunc K)
    where
  inv_zero := by frac_tac
  div := (· / ·)
  div_eq_mul_inv := by frac_tac
  mul_inv_cancel _ := mul_inv_cancel
  zpow := zpowRec
  nnqsmul := _
  nnqsmul_def := fun _ _ => rfl
  qsmul := _
  qsmul_def := fun _ _ => rfl

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