Theorems · Theorem · real analysis
Real.rpow_sub
∀ {x : ℝ}, 0 < x → ∀ (y z : ℝ), x ^ (y - z) = x ^ y / x ^ z- Cited by
- 8 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- le_of_ltproof · cited by 1,175
- sub_eq_add_negproof · cited by 1,023
- div_eq_mul_invproof · cited by 715
- Real.rpow_addproof · cited by 41
- Real.rpow_negproof · cited by 36
Cited by8
Results whose statement or proof uses this declaration.
- strictConvexOn_rpowproof · cited by 2
- Behrend.roth_lower_bound_explicitproof · cited by 1
- Real.tendsto_integral_gaussian_smul'proof · cited by 1
- Real.rpowIntegrand₀₁_one_ge_rpow_sub_twoproof · cited by 1
- Bertrand.real_main_inequalityproof · cited by 1
- sum_div_pow_sq_le_div_sqproof · cited by 1
- Real.summable_nat_rpow_invproof · cited by 1
- NNReal.rpow_subproof · cited by 0