Theorems · Theorem · order theory
iInf_congr_Prop
∀ {α : Type u_1} [inst : InfSet α] {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q),
(∀ (x : q), f₁ ⋯ = f₂ x) → iInf f₁ = iInf f₂- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 218 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 13 definitions · uses propext, Quot.sound
- Assumes
- InfSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by218
Results whose statement or proof uses this declaration.
- Set.iInter_congr_Propproof · cited by 170
- Polynomial.mem_degreeLTproof · cited by 14
- MeasureTheory.extend_eqproof · cited by 10
- nhds_eq_orderproof · cited by 9
- iInf_univproof · cited by 8
- Metric.infEDist_imageproof · cited by 7
- StieltjesFunction.length_eqproof · cited by 7
- Filter.cocompact_eq_cofiniteproof · cited by 7
- Filter.nhds_eqproof · cited by 6
- IsLocalization.height_underproof · cited by 6
- TopologicalSpace.IsTopologicalBasis.of_hasBasis_nhdsproof · cited by 6
- Ideal.sup_iInf_eq_topproof · cited by 5
Showing the 200 most cited of 218.