Theorems · Theorem · order theory
Finset.sup_inf_distrib_left
∀ {α : Type u_2} {ι : Type u_5} [inst : DistribLattice α] [inst_1 : OrderBot α] (s : Finset ι) (f : ι → α) (a : α),
a ⊓ s.sup f = s.sup fun i => a ⊓ f i- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DistribLatticeOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Bot.botproof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Finset.supstatement and proof · cited by 530
- Finset.consproof · cited by 221
- DistribLatticestatement and proof · cited by 150
- Finset.cons_inductionproof · cited by 85
- Finset.sup_emptyproof · cited by 72
- Finset.sup_consproof · cited by 30
- inf_sup_leftproof · cited by 28
- inf_bot_eqproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Finset.disjoint_sup_rightproof · cited by 2
- Finset.sup_inf_distrib_rightproof · cited by 2
- Finset.sup_inf_supproof · cited by 1
- disjointed_eq_selfproof · cited by 1