Theorems · Theorem · order theory
WithBot.le_of_add_le_add_left
∀ {α : Type u} [inst : Add α] {x y z : WithBot α} [inst_1 : LE α] [AddLeftReflectLE α], x ≠ ⊥ → x + y ≤ x + z → y ≤ z- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- AddLEAddLeftReflectLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddLeftReflectLEstatement and proof · cited by 119
- WithBot.recBotCoeproof · cited by 101
- WithBot.add_botproof · cited by 20
- le_of_add_le_add_leftproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- WithBot.addLECancellable_of_ne_botproof · cited by 3
- WithBot.add_le_add_iff_leftproof · cited by 1
- minpoly.IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvdproof · cited by 0