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Theorems · Theorem · combinatorics

Finset.op_vadd_stabilizer_of_no_doubling

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : DecidableEq G] {A : Finset G} {a : G},
  (A + A).card ≤ A.card → a ∈ A → AddOpposite.op a +ᵥ ↑(AddAction.stabilizer G A) = ↑A

A non-empty set with no doubling is the right translate of its stabilizer.

Defined in
Mathlib.Combinatorics.Additive.VerySmallDoubling
Cited by
0 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupDecidableEq
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Set · cited by 53352SetFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupFinset.card · cited by 2327Finset.cardHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddOpposite · cited by 452AddOppositeSet.vaddSet · cited by 403Set.vaddSetAddOpposite.op · cited by 192AddOpposite.opFinset.add · cited by 133Finset.addAddAction.stabilizer · cited by 112AddAction.stabilizerFinset.addActionFinset · cited by 10Finset.addActionFinsetFinset.op_vadd_stabilizer_of_…CITED BYCITES

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