Theorems · Theorem · real analysis
EReal.add_top_of_ne_bot
∀ {x : EReal}, x ≠ ⊥ → x + ⊤ = ⊤For any extended real number x which is not ⊥, the sum of x and ⊤ is equal to ⊤.
- Defined in
- Mathlib.Data.EReal.Operations
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Bot.botstatement and proof · cited by 4,720
- add_commproof · cited by 1,535
- ERealstatement and proof · cited by 793
- EReal.top_add_of_ne_botproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- ENNReal.log_mul_addproof · cited by 4
- EReal.left_distrib_of_nonneg_of_ne_topproof · cited by 2
- 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.exp_addproof · cited by 0
- EReal.limsup_add_le_of_leproof · cited by 0
- EReal.add_ne_top_iff_ne_top₂proof · cited by 0