Theorems · Theorem · real analysis
NNReal.rpow_zero
∀ (x : NNReal), x ^ 0 = 1
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealproof · cited by 1,260
- NNReal.eqproof · cited by 201
- Real.rpow_zeroproof · cited by 69
Cited by20
Results whose statement or proof uses this declaration.
- ENNReal.rpow_zeroproof · cited by 47
- ENNReal.coe_rpow_of_nonnegproof · cited by 34
- CFC.rpow_zeroproof · cited by 8
- CFC.nnrpow_zeroproof · cited by 4
- NNReal.continuousAt_rpow_constproof · cited by 3
- NNReal.rpow_posproof · cited by 3
- ENNReal.toNNReal_rpowproof · cited by 2
- NNReal.rpow_add_le_add_rpowproof · cited by 2
- NNReal.inner_le_weight_mul_Lpproof · cited by 2
- NNReal.zero_rpow_defproof · cited by 1
- NNReal.monotone_rpow_of_nonnegproof · cited by 1
- NNReal.rpow_sum_le_const_mul_sum_rpowproof · cited by 1