Theorems · Theorem · order theory
AddLECancellable.add_le_add_iff_left
∀ {α : Type u_1} [inst : LE α] [inst_1 : Add α] [AddLeftMono α] {a b c : α},
AddLECancellable a → (a + b ≤ a + c ↔ b ≤ c)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- LEAddAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddLeftMonostatement and proof · cited by 687
- AddLECancellablestatement and proof · cited by 87
- add_le_add_rightproof · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- AddLECancellable.add_le_add_iff_rightproof · cited by 4
- AddLECancellable.add_le_iff_nonpos_rightproof · cited by 2
- AddLECancellable.le_add_iff_nonneg_rightproof · cited by 1