Mathlib Map

Theorems · Definition · number theory

UpperHalfPlane.re

UpperHalfPlane → ℝ

Real part

Defined in
Mathlib.Analysis.Complex.UpperHalfPlane.Basic
Cited by
63 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
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Around this declaration

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

UpperHalfPlane.center · cited by 20UpperHalfPlane.centerModularGroup.fd · cited by 17ModularGroup.fdModularGroup.fdo · cited by 13ModularGroup.fdoUpperHalfPlane.verticalStrip · cited by 11UpperHalfPlane.verticalSt…UpperHalfPlane.norm_exp_two_pi_I_lt_one · cited by 7UpperHalfPlane.norm_exp_t…EisensteinSeries.r1 · cited by 6EisensteinSeries.r1UpperHalfPlane.continuous_re · cited by 4UpperHalfPlane.continuous…UpperHalfPlane.toSL2R · cited by 4UpperHalfPlane.toSL2RModularGroup.fdo_subset_fd · cited by 3ModularGroup.fdo_subset_fdModularGroup.re_T_zpow_smul · cited by 3ModularGroup.re_T_zpow_sm…ModularGroup.exists_smul_mem_fd · cited by 2ModularGroup.exists_smul_…ModularGroup.re_T_smul · cited by 2ModularGroup.re_T_smulModularGroup.three_le_four_mul_im_sq_of_mem_fd · cited by 2ModularGroup.three_le_fou…UpperHalfPlane.I_re · cited by 2UpperHalfPlane.I_reUpperHalfPlane.coe_toSL2R · cited by 2UpperHalfPlane.coe_toSL2RReal · cited by 25697RealComplex.re · cited by 882Complex.reUpperHalfPlane · cited by 626UpperHalfPlaneUpperHalfPlane.coe · cited by 288UpperHalfPlane.coeUpperHalfPlane.reCITED BYCITES

Cites4

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

Cited by69

Results whose statement or proof uses this declaration.