Theorems · Theorem · combinatorics
Finset.subset_insert
∀ {α : Type u_1} [inst : DecidableEq α] (a : α) (s : Finset α), s ⊆ insert a s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.mem_insert_of_memproof · cited by 109
Cited by36
Results whose statement or proof uses this declaration.
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- Finset.card_dvd_card_image₂_rightproof · cited by 6
- MeasureTheory.SimpleFunc.FinMeasSupp.of_lintegral_ne_topproof · cited by 4
- eq_affineCombination_of_mem_affineSpanproof · cited by 4
- Finpartition.parts_subset_extendOfLEproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- Set.Intersecting.isUpperSet'proof · cited by 2
- Set.Intersecting.is_max_iff_card_eqproof · cited by 2
- Finset.sum_involutionproof · cited by 2
- Finset.induction_on_pi_of_choiceproof · cited by 2
- Finset.sup_le_of_le_directedproof · cited by 2
- MeasureTheory.IsProjectiveMeasureFamily.eq_zero_of_isEmptyproof · cited by 2