Theorems · Theorem · global analysis

smoothSheafCommRing.eval_germ

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {EM : Type u_2} [inst_1 : NormedAddCommGroup EM]
  [inst_2 : NormedSpace 𝕜 EM] {HM : Type u_3} [inst_3 : TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
  {E : Type u_4} [inst_4 : NormedAddCommGroup E] [inst_5 : NormedSpace 𝕜 E] {H : Type u_5} [inst_6 : TopologicalSpace H]
  {I : ModelWithCorners 𝕜 E H} {M : Type u} [inst_7 : TopologicalSpace M] [inst_8 : ChartedSpace HM M] {R : Type u}
  [inst_9 : TopologicalSpace R] [inst_10 : ChartedSpace H R] [inst_11 : CommRing R] [inst_12 : ContMDiffRing I (↑⊤) R]
  (U : TopologicalSpace.Opens M) (x : M) (hx : x ∈ U)
  (f : ↑((smoothSheafCommRing IM I M R).presheaf.obj (Opposite.op U))),
  (smoothSheafCommRing.eval IM I M R x)
      ((CategoryTheory.ConcreteCategory.hom ((smoothSheafCommRing IM I M R).presheaf.germ U x hx)) f) =
    ↑f ⟨x, hx⟩

Defined in

Mathlib.Geometry.Manifold.Sheaf.Smooth

Cited by

1 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceCommRingContMDiffRing