`brgcGrayCover`

definition

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module: IndisputableMonolith.Patterns.GrayCycleBRGC
domain: Patterns
line: 431 · github
papers citing: none yet

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IndisputableMonolith.Patterns.GrayCycleBRGC on GitHub at line 431.

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formal source

 428  oneBit_step := brgc_oneBit_step (d := d) hdpos
 429}
 430
 431noncomputable def brgcGrayCover (d : Nat) (hdpos : 0 < d) : GrayCover d (2 ^ d) :=
 432{ path := brgcPath d
 433  complete := by
 434    classical
 435    have h_inj : Function.Injective (brgcPath d) := brgcPath_injective d
 436    have h_card : Fintype.card (Fin (2 ^ d)) = Fintype.card (Pattern d) := by
 437      simp [Patterns.card_pattern]
 438    have h_bij : Function.Bijective (brgcPath d) :=
 439      (Fintype.bijective_iff_injective_and_card (brgcPath d)).2 ⟨h_inj, h_card⟩
 440    exact h_bij.2
 441  oneBit_step := brgc_oneBit_step (d := d) hdpos
 442}
 443
 444end GrayCycleBRGC
 445
 446end Patterns
 447end IndisputableMonolith

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