Theorems · Theorem · functional analysis
norm_smul_of_nonneg
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {t : ℝ},
0 ≤ t → ∀ (x : E), ‖t • x‖ = t * ‖x‖- Cited by
- 7 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- abs_of_nonnegproof · cited by 279
- norm_smulproof · cited by 242
- Real.norm_eq_absproof · cited by 88
Cited by7
Results whose statement or proof uses this declaration.
- SameRay.norm_addproof · cited by 7
- exists_dist_eqproof · cited by 3
- SameRay.norm_subproof · cited by 2
- exists_forall_closed_ball_dist_add_le_two_subproof · cited by 1
- SameRay.norm_smul_eqproof · cited by 1
- hasFDerivAt_integral_of_dominated_loc_of_lip'proof · cited by 1
- exists_forall_closed_ball_dist_add_le_two_mul_subproof · cited by 0