leadingCoeff_toLex — Mathlib

English

If p.vars ⊆ range f and f is injective, there exists q with rename f q = p.

Русский

Если p.vars ⊆ range f и f инъективно, существует q такое, что rename f q = p.

LaTeX

$$$ \exists q, rename\ f\ q = p $$$

Lean4

theorem leadingCoeff_toLex : p.leadingCoeff toLex = p.coeff (ofLex <| p.supDegree toLex) :=
  by
  rw [leadingCoeff]
  apply congr_arg p.coeff
  apply toLex.injective
  rw [Function.rightInverse_invFun toLex.surjective, toLex_ofLex]

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