Theorems · Theorem · global analysis

mfderivWithin_comp_projIcc_one

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_2} [inst_2 : TopologicalSpace H]
  {I : ModelWithCorners ℝ E H} {M : Type u_3} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M] {x y : ℝ}
  [h : Fact (x < y)] {f : ↑(Set.Icc x y) → M} {w : ↑(Set.Icc x y)},
  (mfderiv[Set.Icc x y] (f ∘ Set.projIcc x y ⋯) ↑w) 1 = (mfderiv% f w) 1

Defined in

Mathlib.Geometry.Manifold.Instances.Icc

Cited by

1 results in Mathlib

Foundations

Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFact