Theorems · Theorem · order theory
WithBot.add_left_inj
∀ {α : Type u} [inst : Add α] {x y z : WithBot α} [IsLeftCancelAdd α], x ≠ ⊥ → (x + y = x + z ↔ y = z)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddIsLeftCancelAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsLeftCancelAddstatement and proof · cited by 72
- WithBot.add_botproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- WithBot.add_left_cancelproof · cited by 0