Theorems · Theorem · order theory
iInf_or
∀ {α : Type u_1} [inst : CompleteLattice α] {p q : Prop} {s : p ∨ q → α},
⨅ (x : p ∨ q), s x = (⨅ (i : p), s ⋯) ⊓ ⨅ (j : q), s ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_infproof · cited by 107
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- ge_antisymmproof · cited by 51
- inf_le_of_left_leproof · cited by 17
- inf_le_of_right_leproof · cited by 10
- le_iInf_compproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- nhds_eq_orderproof · cited by 9
- iInf_unionproof · cited by 5
- iInf_insertproof · cited by 5
- Set.iInter_orproof · cited by 1
- egauge_unionproof · cited by 0