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Theorems · Theorem · order theory

Right.add_pos_of_pos_of_nonneg

∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddRightStrictMono α] {a b : α},
  0 < a → 0 ≤ b → 0 < a + b

Assumes right covariance. The lemma assuming left covariance is Left.add_pos_of_pos_of_nonneg.

Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
AddZeroClassPreorderAddRightStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Right.pos_add_of_left · cited by 0Right.pos_add_of_leftPreorder · cited by 7952PreorderAddZeroClass · cited by 1237AddZeroClassAddRightStrictMono · cited by 160AddRightStrictMonolt_add_of_pos_of_le · cited by 6lt_add_of_pos_of_leRight.add_pos_of_pos_of_nonnegCITED BYCITES

Cites4

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Cited by1

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