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structure definition def or abbrev

PeanoSurface

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formal statement (Lean)

  72structure PeanoSurface {R : LogicRealization} (A : ArithmeticOf R) : Prop where
  73  zero_ne_step : ∀ x : A.peano.carrier, A.peano.zero ≠ A.peano.step x
  74  step_injective : Function.Injective A.peano.step
  75  induction :
  76    ∀ P : A.peano.carrier → Prop,
  77      P A.peano.zero →
  78      (∀ n, P n → P (A.peano.step n)) →
  79      ∀ n, P n
  80
  81/-! ## LogicNat as the canonical initial Peano object -/
  82
  83/-- The Peano object carried by `LogicNat`. -/

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