Theorems · Theorem · order theory
add_le_add_left
∀ {α : Type u_1} [inst : Add α] [inst_1 : LE α] [i : AddRightMono α] {b c : α}, b ≤ c → ∀ (a : α), b + a ≤ c + a- Cited by
- 37 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLEAddRightMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddRightMonostatement and proof · cited by 367
- CovariantClass.elimproof · cited by 22
Cited by37
Results whose statement or proof uses this declaration.
- add_le_addproof · cited by 666
- le_add_of_nonneg_leftproof · cited by 37
- add_lt_add_of_le_of_ltproof · cited by 31
- add_left_monoproof · cited by 9
- add_le_of_nonpos_leftproof · cited by 7
- CanonicallyOrderedAdd.toIsOrderedAddMonoidproof · cited by 5
- le_add_of_nonneg_of_leproof · cited by 5
- lt_add_of_nonneg_of_ltproof · cited by 4
- WithTop.add_le_add_iff_rightproof · cited by 3
- limsup_add_constproof · cited by 2
- cauchy_davenport_minOrder_addproof · cited by 2
- add_lt_of_nonpos_of_ltproof · cited by 2