Theorems · Theorem · order theory
lt_add_of_lt_of_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b c : α}, b < c → 0 ≤ a → b < c + a- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- add_zeroproof · cited by 2,707
- AddZeroClassstatement and proof · cited by 1,237
- AddLeftMonostatement and proof · cited by 687
- add_le_add_rightproof · cited by 37
Cited by6
Results whose statement or proof uses this declaration.
- zero_lt_threeproof · cited by 10
- zero_lt_fourproof · cited by 8
- Left.add_pos_of_pos_of_nonnegproof · cited by 6
- lt_add_of_lt_of_pos'proof · cited by 1
- Finset.card_add_card_subsetSum_lt_card_subsetSum_insert_maxproof · cited by 1
- abs_sub_lt_of_nonneg_of_ltproof · cited by 1