Mathlib Map

Theorems · Theorem · order theory

Left.one_lt_mul_of_left

∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Preorder α] [IsBotOneClass α] [MulLeftMono α] {a : α},
  1 < a → ∀ (b : α), 1 < a * b
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
MulOneClassPreorderIsBotOneClassMulLeftMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

one_lt_mul_of_left · cited by 0one_lt_mul_of_leftPreorder · cited by 7952PreorderMulOneClass · cited by 1018MulOneClassMulLeftMono · cited by 410MulLeftMonoIsBotOneClass · cited by 35IsBotOneClassone_le · cited by 23one_leLeft.one_lt_mul_of_lt_of_le · cited by 2Left.one_lt_mul_of_lt_of_…Left.one_lt_mul_of_leftCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.