Mathlib Map

Theorems · Theorem · order theory

lt_two_mul_self

∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] {a : R} [ZeroLEOneClass R] [MulPosStrictMono R] [NeZero 1]
  [AddLeftStrictMono R], 0 < a → a < 2 * a
Defined in
Mathlib.Algebra.Order.Ring.Unbundled.Basic
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext
Assumes
SemiringPartialOrderZeroLEOneClassMulPosStrictMonoNeZeroAddLeftStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

blimsup_cthickening_ae_le_of_eventually_mul_le_aux · cited by 1blimsup_cthickening_ae_le…MeasureTheory.UniformIntegrable.spec' · cited by 1UniformIntegrable.spec'Semiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderZeroLEOneClass · cited by 304ZeroLEOneClassAddLeftStrictMono · cited by 203AddLeftStrictMonoMulPosStrictMono · cited by 94MulPosStrictMonoone_lt_two · cited by 67one_lt_twolt_mul_of_one_lt_left · cited by 5lt_mul_of_one_lt_leftlt_two_mul_selfCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.