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def

refl

definition
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module
IndisputableMonolith.RRF.Core.Octave
domain
RRF
line
101 · github
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IndisputableMonolith.RRF.Core.Octave on GitHub at line 101.

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formal source

  98namespace OctaveEquiv
  99
 100/-- Reflexivity. -/
 101def refl (O : Octave) : OctaveEquiv O O where
 102  toFun := OctaveMorphism.id O
 103  invFun := OctaveMorphism.id O
 104  strain_eq := fun _ => rfl
 105  strain_eq_inv := fun _ => rfl
 106
 107/-- Symmetry. -/
 108def symm {O₁ O₂ : Octave} (e : OctaveEquiv O₁ O₂) : OctaveEquiv O₂ O₁ where
 109  toFun := e.invFun
 110  invFun := e.toFun
 111  strain_eq := e.strain_eq_inv
 112  strain_eq_inv := e.strain_eq
 113
 114end OctaveEquiv
 115
 116/-- The "octave index" in Z (integer rung number).
 117    This is just a type alias; the physical interpretation is in Hypotheses. -/
 118abbrev OctaveRung := ℤ
 119
 120/-- A family of octaves indexed by rung. -/
 121structure OctaveFamily where
 122  /-- The octave at each rung. -/
 123  octaveAt : OctaveRung → Octave
 124
 125end RRF.Core
 126end IndisputableMonolith