Theorems · Theorem · real analysis
EReal.top_add_of_ne_bot
∀ {x : EReal}, x ≠ ⊥ → ⊤ + x = ⊤For any extended real number x which is not ⊥, the sum of ⊤ and x is equal to ⊤.
- Defined in
- Mathlib.Data.EReal.Operations
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- EReal.top_add_coeproof · cited by 2
- EReal.top_add_topproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- EReal.add_top_of_ne_botproof · cited by 8
- EReal.left_distrib_of_nonneg_of_ne_topproof · cited by 2
- EReal.top_add_iff_ne_botproof · cited by 1
- EReal.add_ne_top_iff_ne_top_leftproof · cited by 1
- EReal.toENNReal_addproof · cited by 0
- EReal.toENNReal_add_leproof · cited by 0
- EReal.sub_lt_sub_of_le_of_gtproof · cited by 0
- EReal.liminf_add_top_of_ne_botproof · cited by 0
- EReal.add_ne_top_iff_ne_top₂proof · cited by 0
- EReal.add_ne_top_iff_of_ne_bot_of_ne_topproof · cited by 0