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Theorems · Theorem · group theory

fixingSubgroup_empty

∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α], fixingSubgroup M ∅ = ⊤
Defined in
Mathlib.GroupTheory.GroupAction.FixingSubgroup
Cited by
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupMulAction
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Around this declaration

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

MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mul · cited by 2IsMultiplyPretransitive.i…SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective · cited by 1SubMulAction.of_fixingSub…Set · cited by 53352SetTop.top · cited by 9680Top.topGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupMulAction · cited by 1294MulActionfixingSubgroup · cited by 83fixingSubgroupGaloisConnection.l_bot · cited by 63GaloisConnection.l_botfixingSubgroup_fixedPoints_gc · cited by 7fixingSubgroup_fixedPoint…fixingSubgroup_emptyCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.