Theorems · Theorem · real analysis
EReal.exists_nat_ge_mul
∀ {a : EReal}, a ≠ ⊤ → ∀ (n : ℕ), ∃ m, a * ↑n ≤ ↑m- Defined in
- Mathlib.Data.EReal.Inv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- Bot.botproof · cited by 4,720
- Nat.cast_zeroproof · cited by 1,870
- ERealstatement and proof · cited by 793
- bot_leproof · cited by 306
- Real.toERealproof · cited by 303
- Nat.cast_nonneg'proof · cited by 245
- exists_nat_geproof · cited by 20
- EReal.coe_le_coe_iffproof · cited by 10
- EReal.coe_coe_eq_natCastproof · cited by 8
- EReal.coe_mulproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- LinearGrowth.EReal.eventually_atTop_exists_nat_betweenproof · cited by 2
- Monotone.le_linearGrowthSup_compproof · cited by 2
- Monotone.linearGrowthInf_comp_leproof · cited by 2