Theorems · Theorem · order theory
AddLECancellable.add_le_add_iff_right
∀ {α : Type u_1} [inst : LE α] [inst_1 : Add α] [IsAddCommutative α] [AddLeftMono α] {a b c : α},
AddLECancellable a → (b + a ≤ c + a ↔ b ≤ c)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsAddCommutativestatement and proof · cited by 40
- add_comm'proof · cited by 7
- AddLECancellable.add_le_add_iff_leftproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.eq_of_subset_of_encard_le'proof · cited by 4
- ENat.WithBot.add_le_add_natCast_right_iffproof · cited by 2
- EReal.le_sub_iff_add_leproof · cited by 2
- EReal.add_lt_add_right_coeproof · cited by 2