Theorems · Theorem · manifolds
sum_chartAt_inl_apply
∀ {H : Type u} {M : Type u_2} {M' : Type u_3} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M]
[inst_2 : TopologicalSpace M'] [cm : ChartedSpace H M] [cm' : ChartedSpace H M'] {x y : M},
↑(chartAt H (Sum.inl x)) (Sum.inl y) = ↑(chartAt H x) y- Defined in
- Mathlib.Geometry.Manifold.ChartedSpace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- ChartedSpacestatement and proof · cited by 2,397
- OpenPartialHomeomorph.toFun'statement and proof · cited by 745
- OpenPartialHomeomorphproof · cited by 664
- chartAtstatement and proof · cited by 301
- Topology.IsOpenEmbedding.inlproof · cited by 11
- ChartedSpace.sum_chartAt_inlproof · cited by 7
- nonempty_of_chartedSpaceproof · cited by 4
- OpenPartialHomeomorph.lift_openEmbedding_applyproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- ContMDiff.sumElimproof · cited by 4
- hasMFDerivWithinAt_inlproof · cited by 2
- Manifold.IsImmersionOfComplement.sumInlproof · cited by 1
- writtenInExtChartAt_sumSwap_eventuallyEq_idproof · cited by 1
- hasMFDerivAt_sumSwapproof · cited by 1
- extChartAt_inl_applyproof · cited by 0