Theorems · Theorem · commutative algebra
IsIntegral.neg
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B},
IsIntegral R x → IsIntegral R (-x)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 132 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.adjoinproof · cited by 535
- IsIntegralstatement and proof · cited by 427
- Algebra.subset_adjoinproof · cited by 109
- IsIntegral.of_mem_of_fgproof · cited by 13
- IsIntegral.fg_adjoin_singletonproof · cited by 13
- Subalgebra.neg_memproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- IsIntegral.coeffproof · cited by 4
- IsIntegral.neg_iffproof · cited by 1
- IsIntegral.of_negproof · cited by 1
- IsIntegral.of_mem_closure'proof · cited by 1