Theorems · Theorem · order theory
Finset.iInf_insert
∀ {α : Type u_2} {β : Type u_3} [inst : CompleteLattice β] [inst_1 : DecidableEq α] (a : α) (s : Finset α) (t : α → β),
⨅ x ∈ insert a s, t x = t a ⊓ ⨅ x ∈ s, t x- Defined in
- Mathlib.Order.CompleteLattice.Finset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.coeproof · cited by 8,199
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_congr_Propproof · cited by 218
- Finset.mem_insertproof · cited by 44
- Set.mem_insert_iffproof · cited by 39
- iInf_insertproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Finset.set_biInter_insertproof · cited by 5
- Ideal.sup_iInf_eq_topproof · cited by 5
- Ideal.prod_eq_iInf_of_pairwise_isCoprimeproof · cited by 4
- Filter.iInf_principal_finsetproof · cited by 3
- Finset.iInf_insert_updateproof · cited by 1