Theorems · Theorem · group theory

MulAction.isMultiplyPreprimitive_iff

∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α] (n : ℕ),
  MulAction.IsMultiplyPreprimitive M α n ↔
    MulAction.IsMultiplyPretransitive M α n ∧
      ∀ {s : Set α},
        s.encard + 1 = ↑n → MulAction.IsPreprimitive ↥(fixingSubgroup M s) ↥(SubMulAction.ofFixingSubgroup M s)

Defined in: Mathlib.GroupTheory.GroupAction.MultiplePrimitivity
Cited by: 5 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction

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

Cites13

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

Setstatement and proof · cited by 53,352
Groupstatement and proof · cited by 6,238
ENatstatement · cited by 4,985
Subgroupstatement · cited by 3,593
MulActionstatement and proof · cited by 1,294
Set.encardstatement and proof · cited by 327
SubMulActionstatement · cited by 120
fixingSubgroupstatement and proof · cited by 83
MulAction.IsPreprimitivestatement and proof · cited by 50
SubMulAction.ofFixingSubgroupstatement and proof · cited by 43
MulAction.IsMultiplyPretransitivestatement and proof · cited by 33
MulAction.IsMultiplyPreprimitivestatement and proof · cited by 17

Cited by5

Results whose statement or proof uses this declaration.

MulAction.is_one_preprimitive_iffproof · cited by 2
MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 2
MulAction.isMultiplyPreprimitive_ofStabilizerproof · cited by 1
MulAction.isMultiplyPreprimitive_of_isMultiplyPretransitive_succproof · cited by 1
MulAction.isMultiplyPreprimitive_congrproof · cited by 0