Theorems · Theorem · functional analysis
HasSolidNorm.solid
∀ {α : Type u_1} {inst : NormedAddCommGroup α} {inst_1 : Lattice α} [self : HasSolidNorm α] ⦃x y : α⦄,
|x| ≤ |y| → ‖x‖ ≤ ‖y‖- Defined in
- Mathlib.Analysis.Normed.Order.Lattice
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- HasSolidNorm
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.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement · cited by 5,413
- absstatement · cited by 1,814
- Latticestatement and proof · cited by 916
- HasSolidNormstatement and proof · cited by 67
Cited by9
Results whose statement or proof uses this declaration.
- norm_le_norm_of_abs_le_absproof · cited by 6
- norm_abs_eq_normproof · cited by 2
- norm_inf_sub_inf_le_add_normproof · cited by 1
- norm_sup_sub_sup_le_add_normproof · cited by 1
- norm_sup_sub_sup_le_normproof · cited by 1
- LatticeOrderedAddCommGroup.isSolid_ballproof · cited by 0
- norm_inf_sub_inf_le_normproof · cited by 0
- norm_abs_sub_absproof · cited by 0
- dual_solidproof · cited by 0