Theorems · Theorem · order theory
IsAbsoluteValue.abv_sub_le
∀ {S : Type u_5} [inst : Ring S] [inst_1 : PartialOrder S] {R : Type u_6} [inst_2 : Ring R] (abv : R → S)
[IsAbsoluteValue abv] (a b c : R), abv (a - c) ≤ abv (a - b) + abv (b - c)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
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.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- sub_eq_add_negproof · cited by 1,023
- add_assocproof · cited by 746
- IsAbsoluteValuestatement and proof · cited by 160
- neg_add_cancel_leftproof · cited by 84
- IsAbsoluteValue.abv_addproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsCauSeq.cauchy₂proof · cited by 3