Theorems · Theorem · order theory
AbsoluteValue.map_zero
∀ {R : Type u_5} {S : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : PartialOrder S]
(abv : AbsoluteValue R S), abv 0 = 0- Cited by
- 19 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- SemiringSemiringPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- AbsoluteValuestatement and proof · cited by 363
- AbsoluteValue.eq_zeroproof · cited by 5
Cited by19
Results whose statement or proof uses this declaration.
- IsAbsoluteValue.abv_zeroproof · cited by 5
- AbsoluteValue.map_negproof · cited by 4
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- AbsoluteValue.isEquiv_iff_lt_one_iffproof · cited by 3
- Height.mulHeight_sumElim_zero_eqproof · cited by 3
- Height.mulHeight₁_zeroproof · cited by 2
- Height.max_mulHeightBound_zero_one_eq_oneproof · cited by 2
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1
- Rat.AbsoluteValue.equiv_real_of_unboundedproof · cited by 1
- AbsoluteValue.isEquiv_of_lt_one_impproof · cited by 1
- Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_oneproof · cited by 1
- AbsoluteValue.isNontrivial_iff_ne_trivialproof · cited by 1