Theorems · Theorem · order theory
mabs_zpow
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : LinearOrder α] [IsOrderedMonoid α] (n : ℤ) (a : α),
|a ^ n|ₘ = |a|ₘ ^ |n|- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- absstatement and proof · cited by 1,814
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- le_totalproof · cited by 294
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- mabsstatement and proof · cited by 148
- abs_negproof · cited by 93
- neg_nonnegproof · cited by 60
- Nat.abs_castproof · cited by 36
- mabs_invproof · cited by 13
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