Theorems · Theorem · order theory
mabs_pow
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] (n : ℕ) (a : G), |a ^ n|ₘ = |a|ₘ ^ n- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 1 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.
Cites11
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
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- le_totalproof · cited by 294
- mabsstatement and proof · cited by 148
- inv_powproof · cited by 140
- mabs_invproof · cited by 13
- mabs_of_one_leproof · cited by 11
- mabs_of_le_oneproof · cited by 6
- one_le_pow_of_one_le'proof · cited by 6
- one_le_inv'proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- mabs_zpowproof · cited by 0