`samePattern`

definition

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module: IndisputableMonolith.RRF.Theorems.OctaveTransfer
domain: RRF
line: 87 · github
papers citing: none yet

open explainer

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open lean source

IndisputableMonolith.RRF.Theorems.OctaveTransfer on GitHub at line 87.

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explainer page

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depends on

used by

formal source

  84/-! ## The "Same Pattern, Different Scale" Principle -/
  85
  86/-- Two octaves manifest the same pattern if they're equivalent. -/
  87def samePattern (O₁ O₂ : Octave) : Prop :=
  88  Nonempty (OctaveEquiv O₁ O₂)
  89
  90theorem samePattern_refl (O : Octave) : samePattern O O :=
  91  ⟨OctaveEquiv.refl O⟩
  92
  93theorem samePattern_symm {O₁ O₂ : Octave} (h : samePattern O₁ O₂) :
  94    samePattern O₂ O₁ :=
  95  let ⟨e⟩ := h
  96  ⟨OctaveEquiv.symm e⟩
  97
  98end RRF.Theorems
  99end IndisputableMonolith

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