Theorems · Theorem · order theory
DedekindCut.principal_sSup_left
∀ {α : Type u_1} [inst : CompleteLattice α] (A : DedekindCut α), DedekindCut.principal (sSup A.left) = A- Defined in
- Mathlib.Order.Completion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.extproof · cited by 2,266
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- Set.mem_Iciproof · cited by 37
- DedekindCutstatement and proof · cited by 27
- DedekindCut.principalstatement · cited by 20
- mem_upperBoundsproof · cited by 20
- DedekindCut.leftstatement and proof · cited by 16
- DedekindCut.rightproof · cited by 12
- sSup_le_iffproof · cited by 8
- DedekindCut.right_principalproof · cited by 1
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