Theorems · Theorem · group theory
domain_nontrivial
∀ {M₀ : Type u_1} {M₀' : Type u_2} [inst : MulZeroOneClass M₀] [Nontrivial M₀] [inst_2 : Zero M₀'] [inst_3 : One M₀']
(f : M₀' → M₀), f 0 = 0 → f 1 = 1 → Nontrivial M₀'Pullback a Nontrivial instance along a function sending 0 to 0 and 1 to 1.
- Defined in
- Mathlib.Algebra.GroupWithZero.NeZero
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- MulZeroOneClassstatement and proof · cited by 184
- zero_ne_oneproof · cited by 90
Cited by2
Results whose statement or proof uses this declaration.
- Function.Injective.isDomainproof · cited by 27
- Function.Injective.isStrictOrderedRingproof · cited by 0