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Theorems · Theorem · order theory

add_pos_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

Alias of Right.pos_add_of_right.

Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
8 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
AddZeroClassPreorderIsBotZeroClassAddRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Ordinal.opow_add_one · cited by 9Ordinal.opow_add_oneOrdinal.veblenWith_add_one · cited by 3Ordinal.veblenWith_add_oneTestFunction.lineDerivCLM_apply · cited by 2TestFunction.lineDerivCLM…Ordinal.lt_omega0_opow_succ · cited by 1Ordinal.lt_omega0_opow_su…Ordinal.succ_pos · cited by 0Ordinal.succ_posENat.add_one_pos · cited by 0ENat.add_one_posOrdinal.succ_ne_zero · cited by 0Ordinal.succ_ne_zeroOrdinal.add_one_ne_zero · cited by 0Ordinal.add_one_ne_zeroPreorder · cited by 7952PreorderAddZeroClass · cited by 1237AddZeroClassAddRightMono · cited by 367AddRightMonoIsBotZeroClass · cited by 71IsBotZeroClassRight.pos_add_of_right · cited by 1Right.pos_add_of_rightadd_pos_of_rightCITED BYCITES

Cites5

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

Cited by8

Results whose statement or proof uses this declaration.