Theorems · Theorem · real analysis
EReal.top_add_iff_ne_bot
∀ {x : EReal}, ⊤ + x = ⊤ ↔ x ≠ ⊥For any extended real number x, the sum of ⊤ and x is equal to ⊤
if and only if x is not ⊥.
- Defined in
- Mathlib.Data.EReal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 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.
- Realproof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- ERealstatement and proof · cited by 793
- Real.toERealproof · cited by 303
- EReal.recproof · cited by 57
- bot_ne_topproof · cited by 24
- EReal.add_botproof · cited by 12
- EReal.top_add_of_ne_botproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- EReal.add_top_iff_ne_botproof · cited by 1