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Theorems · Theorem · logic and foundations

Ordinal.add_sSup

∀ (o : Ordinal.{u}) {s : Set Ordinal.{u}} [Small.{u, u + 1} ↑s], s.Nonempty → o + sSup s = sSup ((fun x => o + x) '' s)
Defined in
Mathlib.SetTheory.Ordinal.Family
Cited by
0 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Small
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Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.image · cited by 5609Set.imageSet.Nonempty · cited by 2627Set.NonemptyOrdinal · cited by 1688OrdinalSupSet.sSup · cited by 954SupSet.sSupSmall · cited by 369SmallOrdinal.bddAbove_of_small · cited by 19Ordinal.bddAbove_of_smallOrdinal.isNormal_add_right · cited by 13Ordinal.isNormal_add_rightOrder.IsNormal.map_sSup · cited by 5IsNormal.map_sSupOrdinal.add_sSupCITED BYCITES

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