Mathlib Map

Theorems · Theorem · order theory

Right.pos_add_of_right

∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [IsBotZeroClass α] [AddRightMono α] {b : α},
  0 < b → ∀ (a : α), 0 < a + b
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddZeroClassPreorderIsBotZeroClassAddRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

add_pos_of_right · cited by 8add_pos_of_rightPreorder · cited by 7952PreorderAddZeroClass · cited by 1237AddZeroClasszero_le · cited by 382zero_leAddRightMono · cited by 367AddRightMonoRight.add_pos_of_nonneg_of_pos · cited by 137Right.add_pos_of_nonneg_o…IsBotZeroClass · cited by 71IsBotZeroClassRight.pos_add_of_rightCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.