Theorems · Theorem · order theory
neg_one_lt_zero
∀ {R : Type u} [inst : Ring R] [inst_1 : LinearOrder R] [ZeroLEOneClass R] [NeZero 1] [AddLeftStrictMono R], -1 < 0- Cited by
- 14 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- zero_lt_oneproof · cited by 598
- ZeroLEOneClassstatement and proof · cited by 304
- AddLeftStrictMonostatement and proof · cited by 203
- neg_lt_zeroproof · cited by 36
Cited by14
Results whose statement or proof uses this declaration.
- integral_exp_neg_rpowproof · cited by 2
- Real.summable_log_one_add_of_summableproof · cited by 2
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2
- Real.doublingGamma_log_convex_Ioiproof · cited by 1
- Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_detproof · cited by 1
- Real.not_differentiableAt_inv_log_zeroproof · cited by 1
- Real.multipliable_one_add_of_summableproof · cited by 1
- rpow_one_add_lt_one_add_mul_selfproof · cited by 1
- Pell.Solution₁.x_ne_zeroproof · cited by 1
- tendsto_pow_const_mul_const_pow_of_lt_oneproof · cited by 1
- Complex.betaIntegral_symmproof · cited by 0
- Real.summable_exp_neg_natproof · cited by 0