Theorems · Theorem · real analysis
NNReal.iSup_eq_zero
∀ {ι : Sort u_1} {f : ι → NNReal}, BddAbove (Set.range f) → (⨆ i, f i = 0 ↔ ∀ (i : ι), f i = 0)- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- Set.rangestatement and proof · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- iSupstatement and proof · cited by 2,415
- IsEmptyproof · cited by 759
- BddAbovestatement and proof · cited by 620
- isEmpty_or_nonemptyproof · cited by 269
- bot_eq_zero'proof · cited by 92
- ciSup_of_emptyproof · cited by 23
- ciSup_le_iffproof · cited by 6
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