Theorems · Theorem · functional analysis
one_le_norm_one
∀ (β : Type u_5) [inst : NormedRing β] [Nontrivial β], 1 ≤ ‖1‖
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Nontrivialstatement and proof · cited by 2,416
- NormedRingstatement and proof · cited by 924
- one_ne_zeroproof · cited by 885
- norm_pos_iffproof · cited by 168
- norm_mul_leproof · cited by 31
- le_mul_iff_one_le_leftproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- tsum_geometric_le_of_norm_lt_oneproof · cited by 1
- one_le_nnnorm_oneproof · cited by 0