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Theorems · Theorem · number theory

UpperHalfPlane.im_pos

∀ (z : UpperHalfPlane), 0 < z.im
Defined in
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
Cited by
62 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UpperHalfPlane.im_ne_zero · cited by 18UpperHalfPlane.im_ne_zeroUpperHalfPlane.mdifferentiableAt_iff · cited by 9UpperHalfPlane.mdifferent…UpperHalfPlane.modular_S_smul · cited by 9UpperHalfPlane.modular_S_…UpperHalfPlane.im_inv_neg_coe_pos · cited by 7UpperHalfPlane.im_inv_neg…UpperHalfPlane.norm_qParam_lt_one · cited by 5UpperHalfPlane.norm_qPara…UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center · cited by 5UpperHalfPlane.cmp_dist_e…UpperHalfPlane.specialLinearGroup_apply · cited by 4UpperHalfPlane.specialLin…UpperHalfPlane.im_pos_of_dist_center_le · cited by 3UpperHalfPlane.im_pos_of_…UpperHalfPlane.cosh_half_dist · cited by 3UpperHalfPlane.cosh_half_…UpperHalfPlane.tendsto_smul_atImInfty · cited by 2UpperHalfPlane.tendsto_sm…EisensteinSeries.D2_mul · cited by 2EisensteinSeries.D2_mulUpperHalfPlane.dist_coe_center_sq · cited by 2UpperHalfPlane.dist_coe_c…UpperHalfPlane.dist_of_re_eq · cited by 2UpperHalfPlane.dist_of_re…UpperHalfPlane.dist_self_center · cited by 2UpperHalfPlane.dist_self_…UpperHalfPlane.eq_zero_of_frequently · cited by 2UpperHalfPlane.eq_zero_of…Real · cited by 25697RealUpperHalfPlane · cited by 626UpperHalfPlaneUpperHalfPlane.im · cited by 128UpperHalfPlane.imUpperHalfPlane.coe_im_pos · cited by 19UpperHalfPlane.coe_im_posUpperHalfPlane.im_posCITED BYCITES

Cites4

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

Cited by62

Results whose statement or proof uses this declaration.