Theorems · Theorem · real analysis
ENNReal.le_mul_of_forall_lt
∀ {a b c : ENNReal}, a ≠ 0 ∨ b ≠ ⊤ → a ≠ ⊤ ∨ b ≠ 0 → (∀ a' > a, ∀ b' > b, c ≤ a' * b') → c ≤ a * b- Defined in
- Mathlib.Data.ENNReal.Inv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- LE.le.trans_eqproof · cited by 328
- LT.lt.ne_topproof · cited by 34
- ENNReal.mul_invproof · cited by 12
- ENNReal.inv_le_invproof · cited by 6
- ENNReal.le_inv_iff_le_invproof · cited by 3
- ENNReal.lt_inv_iff_lt_invproof · cited by 3
- ENNReal.mul_le_of_forall_ltproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.limsup_mul_le'proof · cited by 0
- ENNReal.liminf_mul_leproof · cited by 0