Theorems · Theorem · real analysis
EReal.le_mul_of_forall_lt
∀ {a b c : EReal}, 0 < a ∨ b ≠ ⊤ → a ≠ ⊤ ∨ 0 < b → (∀ a' > a, ∀ b' > b, c ≤ a' * b') → c ≤ a * b- Defined in
- Mathlib.Data.EReal.Inv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Set.Iooproof · cited by 1,214
- LT.lt.neproof · cited by 872
- ERealstatement and proof · cited by 793
- ne_of_gtproof · cited by 637
- LT.lt.transproof · cited by 370
- Set.mem_Iooproof · cited by 29
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- LinearGrowth.linearGrowthSup_comp_leproof · cited by 2
- Monotone.linearGrowthInf_comp_leproof · cited by 2
- EReal.limsup_mul_leproof · cited by 0
- EReal.liminf_mul_leproof · cited by 0