Theorems · Theorem · order theory
mul_le_of_le_one_right
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [PosMulMono α],
0 ≤ a → b ≤ 1 → a * b ≤ a- Cited by
- 29 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
- mul_le_mul_of_nonneg_leftproof · cited by 361
- PosMulMonostatement and proof · cited by 165
Cited by29
Results whose statement or proof uses this declaration.
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- FormalMultilinearSeries.norm_mul_pow_le_of_lt_radiusproof · cited by 6
- HasFPowerSeriesWithinOnBall.uniform_geometric_approx'proof · cited by 3
- mul_lt_one_of_nonneg_of_lt_one_leftproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3
- zpow_right_anti₀proof · cited by 3
- norm_jacobiTheta₂_term_fderiv_leproof · cited by 2
- ContinuousLinearMap.rayleighQuotient_le_normproof · cited by 2
- Real.abs_mulExpNegMulSq_leproof · cited by 2
- Seminorm.gauge_ballproof · cited by 2
- FormalMultilinearSeries.ofScalars_norm_leproof · cited by 2
- exists_continuous_one_zero_of_isCompact_of_isGδproof · cited by 2