Mathlib Map

Theorems · Theorem · number theory

UpperHalfPlane.im_ne_zero

∀ (z : UpperHalfPlane), z.im ≠ 0
Defined in
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
Cited by
18 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.

UpperHalfPlane.denom_ne_zero · cited by 15UpperHalfPlane.denom_ne_z…UpperHalfPlane.ne_zero · cited by 7UpperHalfPlane.ne_zeroEisensteinSeries.D2_mul · cited by 2EisensteinSeries.D2_mulUpperHalfPlane.petersson_continuous · cited by 2UpperHalfPlane.petersson_…UpperHalfPlane.linear_ne_zero · cited by 2UpperHalfPlane.linear_ne_…ModularGroup.cases_of_mem_fd_smul_mem_fd · cited by 2ModularGroup.cases_of_mem…UpperHalfPlane.dist_of_re_eq · cited by 2UpperHalfPlane.dist_of_re…ModularGroup.exists_max_im · cited by 1ModularGroup.exists_max_imModularGroup.exists_one_half_le_im_smul_and_norm_denom_le · cited by 1ModularGroup.exists_one_h…UpperHalfPlane.isElliptic_of_exists_smul_eq_self · cited by 1UpperHalfPlane.isElliptic…UpperHalfPlane.denom_cocycle' · cited by 1UpperHalfPlane.denom_cocy…UpperHalfPlane.mul_smul' · cited by 1UpperHalfPlane.mul_smul'ModularGroup.exists_bound_fundamental_domain_of_isBigO · cited by 1ModularGroup.exists_bound…ModularFormClass.exists_bound · cited by 1ModularFormClass.exists_b…UpperHalfPlane.int_div_mem_integerComplement · cited by 0UpperHalfPlane.int_div_me…Real · cited by 25697RealLT.lt.ne' · cited by 1417lt.ne'UpperHalfPlane · cited by 626UpperHalfPlaneUpperHalfPlane.im · cited by 128UpperHalfPlane.imUpperHalfPlane.im_pos · cited by 62UpperHalfPlane.im_posUpperHalfPlane.im_ne_zeroCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.