Theorems · Theorem · order theory
WithBot.add_eq_bot
∀ {α : Type u} [inst : Add α] {x y : WithBot α}, x + y = ⊥ ↔ x = ⊥ ∨ y = ⊥- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- Add
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.
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- WithBot.someproof · cited by 541
- WithBot.recBotCoeproof · cited by 101
- WithBot.add_botproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Monic.mul_left_ne_zeroproof · cited by 2
- Polynomial.Monic.mul_right_ne_zeroproof · cited by 1
- EReal.add_eq_bot_iffproof · cited by 0