Theorems · Theorem · number theory
NNRat.cast_pow
∀ {K : Type u_1} [inst : DivisionSemiring K] (q : ℚ≥0) (n : ℕ), ↑(q ^ n) = ↑q ^ n- Defined in
- Mathlib.Data.Rat.Cast.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- NNRatstatement and proof · cited by 523
- NNRat.caststatement and proof · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- inv_powproof · cited by 140
- Nat.cast_powproof · cited by 131
- NNRat.numproof · cited by 53
- NNRat.denproof · cited by 51
- Nat.cast_commuteproof · cited by 24
- Commute.mul_powproof · cited by 22
- NNRat.cast_defproof · cited by 17
- NNRat.den_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NNRat.cast_zpow_of_ne_zeroproof · cited by 0