Theorems · Theorem · combinatorics
Finset.insert_subset_iff
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Finset α} {a : α}, insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 57 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.
Cites1
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
Cited by14
Results whose statement or proof uses this declaration.
- Finset.insert_subsetproof · cited by 4
- Finset.induction_on'proof · cited by 3
- Turing.PartrecToTM2.trStmts₁_supportsproof · cited by 2
- Finset.sum_powerset_insertproof · cited by 2
- Finset.ruzsa_covering_addproof · cited by 2
- Finset.ruzsa_covering_mulproof · cited by 2
- Finset.sum_lt_sum_of_subsetproof · cited by 2
- Finset.sum_involutionproof · cited by 2
- Finset.card_add_card_subsetSum_lt_card_subsetSum_insert_maxproof · cited by 1
- Finset.mem_upShadow_iterate_iff_exists_cardproof · cited by 1
- Lagrange.interpolate_eq_sum_interpolate_insert_sdiffproof · cited by 1
- Lagrange.interpolate_eq_add_interpolate_eraseproof · cited by 0