symm_trans_mem_analyticGroupoid — Mathlib

English

For any x ∈ ZMod n, x.valMinAbs = 0 if and only if x = 0.

Русский

Для любого x ∈ ZMod n, x.valMinAbs = 0 тогда и только тогда, когда x = 0.

LaTeX

$$$x.valMinAbs = 0 \\iff x = 0$$$

Lean4

/-- The composition of an open partial homeomorphism from `H` to `M` and its inverse belongs to
the analytic groupoid. -/
theorem symm_trans_mem_analyticGroupoid (e : OpenPartialHomeomorph M H) : e.symm.trans e ∈ analyticGroupoid I :=
  haveI : e.symm.trans e ≈ OpenPartialHomeomorph.ofSet e.target e.open_target := OpenPartialHomeomorph.symm_trans_self _
  StructureGroupoid.mem_of_eqOnSource _ (ofSet_mem_analyticGroupoid e.open_target) this

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