Theorems · Theorem · order theory
WithBot.add_bot
∀ {α : Type u} [inst : Add α] (x : WithBot α), x + ⊥ = ⊥- Cited by
- 20 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
Cited by20
Results whose statement or proof uses this declaration.
- Polynomial.degree_mulproof · cited by 25
- EReal.add_botproof · cited by 12
- Polynomial.degree_add_divByMonicproof · cited by 4
- WithBot.add_eq_botproof · cited by 3
- WithBot.le_of_add_le_add_leftproof · cited by 3
- MonomialOrder.withBotDegree_mul_of_left_mem_nonZeroDivisorsproof · cited by 2
- IsAddLeftRegular.withBotproof · cited by 2
- WithBot.add_lt_add_leftproof · cited by 2
- Nat.WithBot.add_eq_one_iffproof · cited by 1
- Nat.WithBot.add_eq_three_iffproof · cited by 1
- Nat.WithBot.add_eq_zero_iffproof · cited by 1
- WithBot.le_add_selfproof · cited by 1