Theorems · Theorem · order theory
iSup_himp_eq
∀ {α : Type u} {ι : Sort w} [inst : Order.Frame α] {a : α} {f : ι → α}, (⨆ x, f x) ⇨ a = ⨅ x, f x ⇨ a- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Frame
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- HImp.himpstatement · cited by 153
- Order.Framestatement and proof · cited by 88
- eq_of_forall_le_iffproof · cited by 65
- inf_iSup_eqproof · cited by 4
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