Theorems · Theorem · group theory
Finset.pow_ssubset_pow_succ_of_pow_ne_closure
∀ {G : Type u_1} [inst : Group G] [inst_1 : DecidableEq G] {X : Finset G} {n : ℕ},
1 ∈ X → X.Nontrivial → ↑X ^ n ≠ ↑(Subgroup.closure ↑X) → X ^ n ⊂ X ^ (n + 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- one_ne_zeroproof · cited by 885
- add_assocproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- Finset.pow_right_strictMonoOnproof · cited by 1