Theorems · Theorem · order theory
AbsoluteValue.map_sub
∀ {R : Type u_3} {S : Type u_4} [inst : CommRing S] [inst_1 : PartialOrder S] [IsOrderedRing S] [inst_3 : Ring R]
(abv : AbsoluteValue R S) [NoZeroDivisors S] (a b : R), abv (a - b) = abv (b - a)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- NoZeroDivisorsstatement and proof · cited by 545
- AbsoluteValuestatement and proof · cited by 363
- neg_subproof · cited by 272
- AbsoluteValue.map_negproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- IsAbsoluteValue.abv_subproof · cited by 3
- Padic.complete'proof · cited by 1
- Polynomial.exists_partition_polynomial_auxproof · cited by 1
- AbsoluteValue.abs_abv_sub_le_abv_subproof · cited by 1
- Padic.complete''proof · cited by 0
- Padic.exi_rat_seq_conv_cauchyproof · cited by 0