Theorems · Theorem · order theory
le_of_mul_le_mul_left
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [PosMulReflectLE α],
a * b ≤ a * c → 0 < a → b ≤ c- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- PosMulReflectLEstatement and proof · cited by 16
- ContravariantClass.elimproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- le_of_mul_le_mul_of_pos_leftproof · cited by 5
- convexOn_of_slope_mono_adjacentproof · cited by 3
- ProbabilityTheory.measure_ge_le_exp_mul_mgfproof · cited by 3
- Filter.Tendsto.atTop_of_const_mul₀proof · cited by 2
- ArchimedeanClass.mk_le_mk_iff_denselyOrderedproof · cited by 1
- NumberField.exists_nat_le_mulHeight₁proof · cited by 1
- one_le_of_le_mul_left₀proof · cited by 1
- PosMulReflectLE.toPosMulStrictMonoproof · cited by 1
- Finset.card_biUnion_le_of_intersectingproof · cited by 0