zero_lt_posForm_iff — Mathlib

English

algebraMap S R (B.rootLength i) = B.form (P.root i) (P.root i).

Русский

algebraMap S R(B.rootLength i) = B.form(P.root i)(P.root i).

LaTeX

$$$ algebraMap S R\\bigl(B.rootLength\\ i\\bigr) = B.form\\bigl(P.root\\ i\\bigr)\\bigl(P.root\\ i\\bigr) $$$

Lean4

theorem zero_lt_posForm_iff {x y : span S (range P.root)} :
    0 < B.posForm x y ↔ ∃ s > 0, algebraMap S R s = B.form x y :=
  by
  refine ⟨fun h ↦ ⟨B.posForm x y, h, by simp⟩, fun ⟨s, h, h'⟩ ↦ ?_⟩
  rw [← B.algebraMap_posForm] at h'
  rwa [← FaithfulSMul.algebraMap_injective S R h']

Похожие утверждения