Theorems · Theorem · order theory
WithBot.le_add_self
∀ {α : Type u} [inst : AddCommMagma α] [inst_1 : LE α] [CanonicallyOrderedAdd α] {x : WithBot α},
x ≠ ⊥ → ∀ (y : WithBot α), y ≤ x + y- Defined in
- Mathlib.Algebra.Order.Monoid.WithTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CanonicallyOrderedAddstatement and proof · cited by 229
- WithBot.recBotCoeproof · cited by 101
- WithBot.coe_le_coeproof · cited by 76
- le_add_selfproof · cited by 51
- AddCommMagmastatement and proof · cited by 32
- WithBot.add_botproof · cited by 20
- WithBot.coe_addproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomialproof · cited by 0