Theorems · Theorem · order theory
lt_iff_exists_pos_add
∀ {α : Type u} [inst : AddZeroClass α] [inst_1 : Preorder α] [ExistsAddOfLE α] {a b : α} [AddLeftStrictMono α]
[AddLeftReflectLT α], a < b ↔ ∃ c, 0 < c ∧ a + c = b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddZeroClassstatement and proof · cited by 1,237
- ExistsAddOfLEstatement and proof · cited by 330
- AddLeftStrictMonostatement and proof · cited by 203
- lt_add_of_pos_rightproof · cited by 51
- AddLeftReflectLTstatement and proof · cited by 33
- exists_pos_add_of_lt'proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- smul_add_smul_lt_smul_add_smulproof · cited by 2