Theorems · Theorem · order theory
Finset.inter_insert_of_mem
∀ {α : Type u_1} [inst : DecidableEq α] {s₁ s₂ : Finset α} {a : α}, a ∈ s₁ → s₁ ∩ insert a s₂ = insert a (s₁ ∩ s₂)- Defined in
- Mathlib.Data.Finset.Lattice.Lemmas
- Cited by
- 4 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.
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.inter_commproof · cited by 25
- Finset.insert_inter_of_memproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- collapse_modularproof · cited by 1
- SSet.horn₂₁.sqproof · cited by 1
- SSet.horn₂₀.sqproof · cited by 1
- Finset.insert_interproof · cited by 0