Theorems · Theorem · real analysis
Real.rpow_add_of_nonneg
∀ {x y z : ℝ}, 0 ≤ x → 0 ≤ y → 0 ≤ z → x ^ (y + z) = x ^ y * x ^ z- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- ne_of_gtproof · cited by 637
- LE.le.eq_or_ltproof · cited by 220
- Real.rpow_zeroproof · cited by 69
- add_pos_of_pos_of_nonnegproof · cited by 63
- Real.rpow_add'proof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Real.rpow_sum_of_nonnegproof · cited by 2
- isNonarchimedean_smoothingFunproof · cited by 1
- NNReal.rpow_add_of_nonnegproof · cited by 1