Theorems · Theorem · order theory
add_pos
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftStrictMono α] {a b : α},
0 < a → 0 < b → 0 < a + bAlias of Left.add_pos.
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- AddZeroClassstatement · cited by 1,237
- AddLeftStrictMonostatement · cited by 203
- Left.add_posproof · cited by 4
Cited by28
Results whose statement or proof uses this declaration.
- Real.HolderTriple.pos'proof · cited by 13
- Real.cosh_posproof · cited by 7
- NNReal.HolderTriple.pos'proof · cited by 6
- Ordnode.balance_eq_balance'proof · cited by 4
- norm_add_lt_of_not_sameRayproof · cited by 3
- exists_dist_lt_ltproof · cited by 3
- SameRay.exists_eq_smul_addproof · cited by 3
- cauchySeq_bddproof · cited by 3
- Real.goldenRatio_posproof · cited by 3
- ProbabilityTheory.beta_posproof · cited by 2
- ENNReal.rpow_add_of_nonnegproof · cited by 2
- Fermat42.ne_zeroproof · cited by 2