Theorems · Theorem · complex analysis
Complex.cpow_one
∀ (x : ℂ), x ^ 1 = x
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- one_ne_zeroproof · cited by 885
- Complex.expproof · cited by 612
- Complex.logproof · cited by 187
- Complex.exp_logproof · cited by 14
- Complex.cpow_defproof · cited by 3
Cited by20
Results whose statement or proof uses this declaration.
- Real.rpow_oneproof · cited by 114
- Complex.cpow_natCastproof · cited by 12
- Complex.cpow_neg_oneproof · cited by 7
- Complex.cpow_intCastproof · cited by 4
- Complex.cpow_nat_inv_powproof · cited by 3
- Complex.hasStrictFDerivAt_cpowproof · cited by 3
- integral_gaussian_complexproof · cited by 2
- Complex.integral_cpow_mul_exp_neg_mul_Ioiproof · cited by 2
- hasSum_mellin_pi_mul_sq'proof · cited by 2
- HurwitzZeta.jacobiTheta₂'_functional_equation'proof · cited by 1
- Complex.GammaSeq_add_one_leftproof · cited by 1
- Complex.GammaSeq_eq_approx_Gamma_integralproof · cited by 1