Theorems · Theorem · order theory
iInf_pos
∀ {α : Type u_1} [inst : CompleteLattice α] {p : Prop} {f : p → α} (hp : p), ⨅ (h : p), f h = f hp- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- ge_antisymmproof · cited by 51
Cited by31
Results whose statement or proof uses this declaration.
- Ideal.mem_sInfproof · cited by 15
- MeasureTheory.extend_eqproof · cited by 10
- iInf_univproof · cited by 8
- iInf_splitproof · cited by 4
- StieltjesFunction.length_emptyproof · cited by 3
- iInf_trueproof · cited by 3
- ProbabilityTheory.bayesRisk_le_iInf'proof · cited by 3
- iInf_diteproof · cited by 2
- iInf_eq_difproof · cited by 2
- iInf_ge_eq_iInf_nat_addproof · cited by 2
- Dynamics.coverMincard_emptyproof · cited by 2
- Submodule.comap_smul'proof · cited by 1