Theorems · Theorem · combinatorics
Finset.mem_sigma
∀ {ι : Type u_1} {α : ι → Type u_2} {s : Finset ι} {t : (i : ι) → Finset (α i)} {a : (i : ι) × α i},
a ∈ s.sigma t ↔ a.fst ∈ s ∧ a.snd ∈ t a.fst- Defined in
- Mathlib.Data.Finset.Sigma
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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.sigmastatement · cited by 69
- Multiset.mem_sigmaproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- Finset.coe_sigmaproof · cited by 5
- Finset.sum_finset_productproof · cited by 3
- Finset.sum_finset_product_rightproof · cited by 3
- DividedPowers.dpow_sum'proof · cited by 2
- Finset.induction_on_pi_of_choiceproof · cited by 2
- Finset.sup_sigmaproof · cited by 1
- Finset.sum_range_diag_flipproof · cited by 1
- Finset.sigma_monoproof · cited by 1
- Finset.sum_sum_Ioi_add_eq_sum_sum_off_diagproof · cited by 0