Theorems · Theorem · order theory
IsAbsoluteValue.abv_add
∀ {S : Type u_5} [inst : Semiring S] [inst_1 : PartialOrder S] {R : Type u_6} [inst_2 : Semiring R] (abv : R → S)
[IsAbsoluteValue abv] (x y : R), abv (x + y) ≤ abv x + abv y- Cited by
- 11 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsAbsoluteValuestatement and proof · cited by 160
- IsAbsoluteValue.abv_add'proof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- CauSeq.abv_pos_of_not_limZeroproof · cited by 6
- CauSeq.add_limZeroproof · cited by 6
- IsCauSeq.boundedproof · cited by 3
- rat_add_continuous_lemmaproof · cited by 2
- rat_mul_continuous_lemmaproof · cited by 2
- Polynomial.tendsto_abv_eval₂_atTopproof · cited by 2
- IsCauSeq.of_abv_leproof · cited by 2
- CauSeq.of_nearproof · cited by 1
- IsAbsoluteValue.abv_sub_leproof · cited by 1
- cauchy_productproof · cited by 1
- CauSeq.equiv_def₃proof · cited by 0