Theorems · Theorem · order theory
pow_pos
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : PartialOrder M₀] {a : M₀} [PosMulStrictMono M₀]
[ZeroLEOneClass M₀], 0 < a → ∀ (n : ℕ), 0 < a ^ n- Cited by
- 292 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 95 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- MonoidWithZerostatement and proof · cited by 456
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulStrictMonostatement and proof · cited by 151
Cited by292
Results whose statement or proof uses this declaration.
- zpow_posproof · cited by 22
- exists_pow_lt_of_lt_oneproof · cited by 16
- pow_right_strictMono₀proof · cited by 8
- Odd.strictMono_powproof · cited by 7
- Real.sin_pi_over_two_pow_succproof · cited by 6
- Real.pi_lower_bound_startproof · cited by 5
- Real.pi_upper_bound_startproof · cited by 5
- Orientation.oangle_addproof · cited by 5
- pow_right_strictAnti₀proof · cited by 5
- Real.sqrtTwoAddSeries_step_downproof · cited by 5
- Real.sqrtTwoAddSeries_step_upproof · cited by 5
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
Showing the 200 most cited of 292.