Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_eq_of_add_nnnorm_lt_max
∀ {S : Type u_1} [inst : SeminormedAddGroup S] [IsUltrametricDist S] {x y : S}, ‖x + y‖₊ < max ‖x‖₊ ‖y‖₊ → ‖x‖₊ = ‖y‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
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- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- LT.lt.neproof · cited by 872
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement and proof · cited by 177
- not_ne_iffproof · cited by 30
- IsUltrametricDist.nnnorm_add_eq_max_of_nnnorm_ne_nnnormproof · cited by 2
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