Theorems · Theorem · general topology
dist_mul_mul_le_of_le
∀ {E : Type u_2} [inst : SeminormedCommGroup E] {a₁ a₂ b₁ b₂ : E} {r₁ r₂ : ℝ},
dist a₁ b₁ ≤ r₁ → dist a₂ b₂ ≤ r₂ → dist (a₁ * a₂) (b₁ * b₂) ≤ r₁ + r₂- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LE.le.transproof · cited by 3,151
- Dist.diststatement and proof · cited by 1,539
- add_le_addproof · cited by 666
- SeminormedCommGroupstatement and proof · cited by 191
- dist_mul_mul_leproof · cited by 3
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