Mathlib Map

Theorems · Theorem · global analysis

ModelWithCorners.left_inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (x : H),
  ↑I.symm (↑I x) = x
Defined in
Mathlib.Geometry.Manifold.IsManifold.Basic
Cited by
56 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContMDiffWithinAt.comp · cited by 18ContMDiffWithinAt.compdifferentiableWithinAt_localInvariantProp · cited by 13differentiableWithinAt_lo…HasMFDerivWithinAt.comp · cited by 7HasMFDerivWithinAt.compcontDiffWithinAtProp_id · cited by 5contDiffWithinAtProp_idFilter.EventuallyEq.mfderivWithin_eq · cited by 5EventuallyEq.mfderivWithi…ModelWithCorners.leftInverse · cited by 4ModelWithCorners.leftInve…HasMFDerivWithinAt.congr_of_eventuallyEq · cited by 4HasMFDerivWithinAt.congr_…Filter.EventuallyEq.mlieBracketWithin_vectorField_eq · cited by 4EventuallyEq.mlieBracketW…ModelWithCorners.contMDiff · cited by 4ModelWithCorners.contMDiffVectorField.mlieBracketWithin_smul_right · cited by 3VectorField.mlieBracketWi…ContMDiff.inl · cited by 3ContMDiff.inlContMDiff.inr · cited by 3ContMDiff.inrcontMDiffWithinAt_iff_source · cited by 3contMDiffWithinAt_iff_sou…hasMFDerivAt_id · cited by 3hasMFDerivAt_idVectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm · cited by 3VectorField.contMDiffWith…TopologicalSpace · cited by 24529TopologicalSpaceNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldModelWithCorners · cited by 2462ModelWithCornersPartialEquiv.toFun · cited by 821PartialEquiv.toFunModelWithCorners.toFun' · cited by 373ModelWithCorners.toFun'ModelWithCorners.symm · cited by 146ModelWithCorners.symmModelWithCorners.toPartialEquiv · cited by 72ModelWithCorners.toPartia…ModelWithCorners.source_eq · cited by 34ModelWithCorners.source_eqPartialEquiv.left_inv' · cited by 6PartialEquiv.left_inv'ModelWithCorners.left_invCITED BYCITES

Cites11

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Cited by57

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