Theorems · Theorem · real analysis
ENNReal.exists_mem_Ioc_zpow
∀ {x y : ENNReal}, x ≠ 0 → x ≠ ⊤ → 1 < y → y ≠ ⊤ → ∃ n, x ∈ Set.Ioc (y ^ n) (y ^ (n + 1))- Defined in
- Mathlib.Data.ENNReal.Inv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- LT.lt.ne'proof · cited by 1,417
- ENNReal.ofNNRealproof · cited by 1,279
- Set.Iocstatement · cited by 971
- zero_lt_oneproof · cited by 598
- LT.lt.transproof · cited by 370
- ENNReal.coe_le_coeproof · cited by 73
- ENNReal.coe_lt_coeproof · cited by 44
- ENNReal.coe_zpowproof · cited by 5
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