Theorems · Theorem · group theory
Submonoid.pi_mem_of_mulSingle_mem_aux
∀ {η : Type u_1} {f : η → Type u_2} [inst : (i : η) → MulOneClass (f i)] {S : Type u_3}
[inst_1 : SetLike S ((i : η) → f i)] [SubmonoidClass S ((i : η) → f i)] [inst_3 : DecidableEq η] (I : Finset η)
{H : S} (x : (i : η) → f i), (∀ i ∉ I, x i = 1) → (∀ i ∈ I, Pi.mulSingle i (x i) ∈ H) → x ∈ H- Defined in
- Mathlib.Algebra.Group.Submonoid.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- SetLikestatement and proof · cited by 1,084
- MulOneClassstatement and proof · cited by 1,018
- Function.updateproof · cited by 502
- Function.update_selfproof · cited by 201
- Function.update_of_neproof · cited by 198
- MulMemClass.mul_memproof · cited by 173
- Finset.induction_onproof · cited by 167
- Pi.mulSinglestatement and proof · cited by 111
- Finset.mem_insert_of_memproof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.pi_mem_of_mulSingle_memproof · cited by 2