Theorems · Theorem · order theory
Even.pow_abs
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsOrderedRing α] {n : ℕ}, Even n → ∀ (a : α), |a| ^ n = a ^ n- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingLinearOrderIsOrderedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- absstatement · cited by 1,814
- IsOrderedRingstatement and proof · cited by 777
- Evenstatement and proof · cited by 444
- Even.pow_nonnegproof · cited by 94
- abs_eq_selfproof · cited by 59
- abs_powproof · cited by 36
Cited by5
Results whose statement or proof uses this declaration.
- pow_eq_pow_iff_of_ne_zeroproof · cited by 2
- fermatLastTheoremWith_nat_int_rat_tfaeproof · cited by 2
- Rat.addSubmonoid_closure_range_powproof · cited by 1
- EisensteinSeries.r_lower_bound_on_verticalStripproof · cited by 1
- pow_abs_two_mulproof · cited by 0