Theorems · Theorem · order theory
add_le_add_right
∀ {α : Type u_1} [inst : Add α] [inst_1 : LE α] [AddLeftMono α] {b c : α}, b ≤ c → ∀ (a : α), a + b ≤ a + c- Cited by
- 37 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLEAddLeftMono
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.
- AddLeftMonostatement and proof · cited by 687
- 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_rightproof · cited by 69
- one_le_twoproof · cited by 44
- add_lt_add_of_lt_of_leproof · cited by 37
- le_add_of_le_of_nonnegproof · cited by 8
- add_right_monoproof · cited by 7
- lt_add_of_lt_of_nonnegproof · cited by 6
- List.apply_prod_le_sum_mapproof · cited by 5
- AddLECancellable.add_le_add_iff_leftproof · cited by 3
- AddLECancellable.of_add_rightproof · cited by 3
- add_le_of_nonpos_rightproof · cited by 3
- add_lt_of_lt_of_nonposproof · cited by 2