Theorems · Theorem · order theory
IsAbsoluteValue.abv_mul
∀ {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
- 7 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_mul'proof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- CauSeq.mul_limZero_rightproof · cited by 5
- CauSeq.mul_limZero_leftproof · cited by 4
- rat_inv_continuous_lemmaproof · cited by 2
- rat_mul_continuous_lemmaproof · cited by 2
- Polynomial.tendsto_abv_eval₂_atTopproof · cited by 2
- IsAbsoluteValue.abvHom'proof · cited by 2
- cauchy_productproof · cited by 1
- CauSeq.mul_not_equiv_zeroproof · cited by 1