Theorems · Theorem · functional analysis
Seminorm.ext
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddGroup E] [inst_2 : SMul 𝕜 E]
{p q : Seminorm 𝕜 E}, (∀ (x : E), p x = q x) → p = q- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingAddGroupSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- AddGroupstatement and proof · cited by 4,410
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- DFunLike.extproof · cited by 240
Cited by17
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.seminorm_eq_bot_of_gtproof · cited by 1
- SeminormFamily.finset_sup_compproof · cited by 1
- Seminorm.finset_sup_smulproof · cited by 1
- Seminorm.sSup_emptyproof · cited by 1
- Seminorm.smul_compproof · cited by 1
- PiTensorProduct.injectiveSeminorm_le_projectiveSeminormproof · cited by 1
- Seminorm.comp_idproof · cited by 1
- Seminorm.zero_compproof · cited by 1
- SeminormFamily.comp_smul_nnrealproof · cited by 0
- Seminorm.ext_iffproof · cited by 0
- LinearMap.toSeminorm_compproof · cited by 0
- Seminorm.smul_infproof · cited by 0