Theorems · Theorem · order theory
Odd.strictMono_pow
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {n : ℕ} [ExistsAddOfLE R],
Odd n → StrictMono fun a => a ^ n- Defined in
- Mathlib.Algebra.Order.Ring.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- add_zeroproof · cited by 2,707
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_addproof · cited by 2,366
- LE.le.trans_ltproof · cited by 795
- add_assocproof · cited by 746
- StrictMonostatement · cited by 706
- Oddstatement and proof · cited by 364
- ExistsAddOfLEstatement and proof · cited by 330
- LE.le.trans_eqproof · cited by 328
- le_totalproof · cited by 294
Cited by7
Results whose statement or proof uses this declaration.
- pow_eq_pow_iff_of_ne_zeroproof · cited by 2
- pow_eq_neg_pow_iffproof · cited by 2
- Odd.pow_injectiveproof · cited by 1
- Odd.pow_le_powproof · cited by 0
- Odd.pow_lt_powproof · cited by 0
- IsPrimitiveRoot.norm_eq_one_of_linearly_orderedproof · cited by 0
- Even.strictConvexOn_powproof · cited by 0