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Theorems · Theorem · order theory

add_lt_iff_neg_left

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

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

sub_lt_self_iff · cited by 8sub_lt_self_iffReal.add_neg_lt_sSup · cited by 1Real.add_neg_lt_sSupadd_zero · cited by 2707add_zeroAddZeroClass · cited by 1237AddZeroClassAddLeftStrictMono · cited by 203AddLeftStrictMonoAddLeftReflectLT · cited by 33AddLeftReflectLTadd_lt_add_iff_left · cited by 30add_lt_add_iff_leftadd_lt_iff_neg_leftCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.