Theorems · Theorem · Lie groups

Filter.map_add_left_nhdsGT

∀ {H : Type x} [inst : TopologicalSpace H] [inst_1 : AddCommGroup H] [inst_2 : PartialOrder H] [IsOrderedAddMonoid H]
  [ContinuousAdd H] {c a : H},
  Filter.map (fun x => c + x) (nhdsWithin a (Set.Ioi a)) = nhdsWithin (c + a) (Set.Ioi (c + a))

Defined in: Mathlib.Topology.Algebra.Group.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace AddCommGroup PartialOrder IsOrderedAddMonoid ContinuousAdd

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DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
AddCommGroupstatement and proof · cited by 12,871
Filterstatement and proof · cited by 8,121
PartialOrderstatement and proof · cited by 6,410
Set.imageproof · cited by 5,609
Set.preimageproof · cited by 4,946
nhdsWithinstatement and proof · cited by 1,912
IsOrderedAddMonoidstatement and proof · cited by 1,659
add_commproof · cited by 1,535
Set.Ioistatement and proof · cited by 1,463

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