Theorems · Theorem · commutative algebra
neg_one_eq_one_iff
∀ {R : Type u_1} [inst : Ring R] [Nontrivial R], -1 = 1 ↔ ringChar R = 2- Defined in
- Mathlib.Algebra.CharP.Two
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Nat.cast_oneproof · cited by 2,501
- Nontrivialstatement and proof · cited by 2,416
- Nat.cast_addproof · cited by 586
- sub_eq_zeroproof · cited by 407
- sub_neg_eq_addproof · cited by 264
- ringCharstatement and proof · cited by 73
- Nat.prime_twoproof · cited by 55
- Nat.dvd_primeproof · cited by 18
- CharTwo.neg_eqproof · cited by 4
- CharP.ringChar_ne_oneproof · cited by 3
- ringChar.dvdproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- orderOf_neg_oneproof · cited by 5
- CharP.orderOf_eq_two_iffproof · cited by 1