Theorems · Theorem · algebraic topology

Bundle.RiemannianMetric.mk.inj

∀ {B : Type u_4} {E : B → Type u_6} {inst : (b : B) → TopologicalSpace (E b)} {inst_1 : (b : B) → AddCommGroup (E b)}
  {inst_2 : (b : B) → Module ℝ (E b)} {inner : (b : B) → E b →L[ℝ] E b →L[ℝ] ℝ}
  {symm : ∀ (b : B) (v w : E b), ((inner b) v) w = ((inner b) w) v}
  {pos : ∀ (b : B) (v : E b), v ≠ 0 → 0 < ((inner b) v) v}
  {continuousAt : ∀ (b : B), ContinuousAt (fun v => ((inner b) v) v) 0}
  {isVonNBounded : ∀ (b : B), Bornology.IsVonNBounded ℝ {v | ((inner b) v) v < 1}}
  {inner_1 : (b : B) → E b →L[ℝ] E b →L[ℝ] ℝ} {symm_1 : ∀ (b : B) (v w : E b), ((inner_1 b) v) w = ((inner_1 b) w) v}
  {pos_1 : ∀ (b : B) (v : E b), v ≠ 0 → 0 < ((inner_1 b) v) v}
  {continuousAt_1 : ∀ (b : B), ContinuousAt (fun v => ((inner_1 b) v) v) 0}
  {isVonNBounded_1 : ∀ (b : B), Bornology.IsVonNBounded ℝ {v | ((inner_1 b) v) v < 1}},
  { inner := inner, symm := symm, pos := pos, continuousAt := continuousAt, isVonNBounded := isVonNBounded } =
      { inner := inner_1, symm := symm_1, pos := pos_1, continuousAt := continuousAt_1,
        isVonNBounded := isVonNBounded_1 } →
    inner = inner_1

Defined in

Mathlib.Topology.VectorBundle.Riemannian

Cited by

1 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound