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Theorems · Theorem · order theory

pos_of_lt_add_right

∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : LT α] [AddLeftReflectLT α] {a b : α}, a < a + b → 0 < b
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddZeroClassLTAddLeftReflectLT
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Around this declaration

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

le_of_forall_pos_le_add · cited by 15le_of_forall_pos_le_addexists_pos_add_of_lt' · cited by 5exists_pos_add_of_lt'AddSubmonoid.fg_of_subtractive · cited by 2AddSubmonoid.fg_of_subtra…HahnSeries.unit_aux · cited by 2HahnSeries.unit_auxadd_zero · cited by 2707add_zeroAddZeroClass · cited by 1237AddZeroClassAddLeftReflectLT · cited by 33AddLeftReflectLTlt_of_add_lt_add_left · cited by 9lt_of_add_lt_add_leftpos_of_lt_add_rightCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.