Theorems · Theorem · group theory
leftAddCoset_mem_leftAddCoset
∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α) {a : α}, a ∈ s → a +ᵥ ↑s = ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.extproof · cited by 2,266
- HVAdd.hVAddstatement · cited by 1,820
- Set.vaddSetstatement · cited by 403
- SetLike.mem_coeproof · cited by 302
- AddSubgroup.neg_memproof · cited by 23
- mem_leftAddCoset_iffproof · cited by 9
- add_mem_cancel_leftproof · cited by 8
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