Theorems · Theorem · order theory
mul_lt_of_lt_one_left
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [MulPosStrictMono α],
0 < b → a < 1 → a * b < b- Cited by
- 7 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
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
- MulPosStrictMonostatement and proof · cited by 94
- mul_lt_mul_of_pos_rightproof · cited by 54
Cited by7
Results whose statement or proof uses this declaration.
- exists_dist_lt_ltproof · cited by 3
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- Affine.Simplex.inv_height_lt_sum_inv_heightproof · cited by 2
- IsClosed.exists_wbtw_isVisibleproof · cited by 1
- Ideal.exist_integer_multiples_notMemproof · cited by 1
- exists_dist_le_ltproof · cited by 1
- rpow_one_add_lt_one_add_mul_selfproof · cited by 1