Theorems · Theorem · order theory
lt_mul_of_one_lt_right
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [PosMulStrictMono α],
0 < a → 1 < b → a < a * b- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- mul_oneproof · cited by 3,885
- MulOneClassstatement and proof · cited by 1,018
- PosMulStrictMonostatement and proof · cited by 151
- mul_lt_mul_of_pos_leftproof · cited by 71
Cited by5
Results whose statement or proof uses this declaration.
- zpow_right_strictMono₀proof · cited by 8
- Nat.sq_mul_squarefree_of_posproof · cited by 3
- IsPGroup.isNilpotentproof · cited by 1
- Nat.mem_properDivisors_iff_existsproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.Support.finiteproof · cited by 0