Theorems · Theorem · group theory
AddAction.isMultiplyPreprimitive_iff
∀ (M : Type u_1) (α : Type u_2) [inst : AddGroup M] [inst_1 : AddAction M α] (n : ℕ),
AddAction.IsMultiplyPreprimitive M α n ↔
AddAction.IsMultiplyPretransitive M α n ∧
∀ {s : Set α},
s.encard + 1 = ↑n → AddAction.IsPreprimitive ↥(fixingAddSubgroup M s) ↥(SubAddAction.ofFixingAddSubgroup M s)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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
- ENatstatement · cited by 4,985
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddActionstatement and proof · cited by 820
- Set.encardstatement and proof · cited by 327
- SubAddActionstatement · cited by 86
- fixingAddSubgroupstatement and proof · cited by 50
- SubAddAction.ofFixingAddSubgroupstatement and proof · cited by 32
- AddAction.IsPreprimitivestatement and proof · cited by 25
- AddAction.IsMultiplyPretransitivestatement and proof · cited by 17
- AddAction.IsMultiplyPreprimitivestatement and proof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- AddAction.isMultiplyPreprimitive_ofStabilizerproof · cited by 1
- AddAction.isMultiplyPreprimitive_of_isMultiplyPretransitive_succproof · cited by 1
- AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 0
- AddAction.is_zero_preprimitive_iffproof · cited by 0
- AddAction.isMultiplyPreprimitive_congrproof · cited by 0