Theorems · Theorem · group theory
Finset.mul_mem_mul
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Mul α] {s t : Finset α} {a b : α}, a ∈ s → b ∈ t → a * b ∈ s * t- Cited by
- 14 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Finset.mulstatement · cited by 155
- Finset.mem_image₂_of_memproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- Finset.mulEnergy_eq_sum_sq'proof · cited by 2
- exists_subalgebra_of_fgproof · cited by 1
- Finset.card_sq_le_card_mul_mulEnergyproof · cited by 1
- Finset.Nontrivial.mul_leftproof · cited by 1
- Equidecomp.IsDecompOn.comp'proof · cited by 1
- Finset.pow_ssubset_pow_succ_of_pow_ne_closureproof · cited by 1
- MeasureTheory.Measure.haar.le_index_mulproof · cited by 1
- Finset.Nontrivial.mul_rightproof · cited by 0
- Finset.le_card_mul_mul_mulEnergyproof · cited by 0
- Finset.le_card_quotient_mul_sq_inter_subgroupproof · cited by 0
- Finset.doubling_lt_golden_ratioproof · cited by 0
- cauchy_davenport_mul_of_linearOrder_isCancelMulproof · cited by 0