Theorems · Theorem · order theory
iSup_congr_Prop
∀ {α : Type u_1} [inst : SupSet α] {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q),
(∀ (x : q), f₁ ⋯ = f₂ x) → iSup f₁ = iSup f₂- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 247 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 13 definitions · uses propext, Quot.sound
- Assumes
- SupSet
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 by247
Results whose statement or proof uses this declaration.
- Set.iUnion_congr_Propproof · cited by 374
- MeasureTheory.lintegral_indicatorproof · cited by 47
- MeasureTheory.lintegral_zero_measureproof · cited by 34
- MeasureTheory.lintegral_smul_measureproof · cited by 20
- MeasureTheory.lintegral_sum_measureproof · cited by 16
- MeasureTheory.lintegral_add_measureproof · cited by 13
- Finset.sup_id_eq_sSupproof · cited by 12
- iSup_insertproof · cited by 10
- RestrictedProduct.continuous_inclusionproof · cited by 8
- iSup_unionproof · cited by 8
- iSup_univproof · cited by 8
- iSup_singletonproof · cited by 7
Showing the 200 most cited of 247.