Theorems · Theorem · commutative algebra
RingHom.IsIntegralElem.sub
∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) {x y : S},
f.IsIntegralElem x → f.IsIntegralElem y → f.IsIntegralElem (x - y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- RingHomstatement and proof · cited by 10,189
- sub_eq_add_negproof · cited by 1,023
- RingHom.IsIntegralElemstatement and proof · cited by 33
- RingHom.IsIntegralElem.addproof · cited by 3
- RingHom.IsIntegralElem.negproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsIntegral.subproof · cited by 7
- exists_isIntegral_sub_of_isIntegralElem_of_mul_mem_rangeproof · cited by 1