Theorems · Theorem · real analysis
ENNReal.zero_rpow_def
∀ (y : ℝ), 0 ^ y = if 0 < y then 0 else if y = 0 then 1 else ⊤
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 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
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- lt_trichotomyproof · cited by 178
- ENNReal.rpow_zeroproof · cited by 47
- ENNReal.zero_rpow_of_posproof · cited by 36
- asymmproof · cited by 12
- ENNReal.zero_rpow_of_negproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.log_rpowproof · cited by 4
- ENNReal.zero_rpow_mul_selfproof · cited by 0