Theorems · Theorem · order theory
iInf_extend_top
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : CompleteLattice α] {e : ι → β},
Function.Injective e → ∀ (f : ι → α), ⨅ j, Function.extend e f ⊤ j = ⨅ i, f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_topproof · cited by 411
- iInf_congr_Propproof · cited by 218
- inf_of_le_leftproof · cited by 186
- Function.extendstatement and proof · cited by 111
- Function.Injective.extend_applyproof · cited by 57
- Function.extend_apply'proof · cited by 30
- iInf_topproof · cited by 21
- iInf_commproof · cited by 12
- iInf_existsproof · cited by 6
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