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theorem proved tactic proof

ordered_faithful

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formal statement (Lean)

  71theorem ordered_faithful :
  72    LogicRealization.FaithfulArithmeticInterpretation natOrderedRealization where
  73  injective := by

proof body

Tactic-mode proof.

  74    intro a b h
  75    exact (ArithmeticFromLogic.LogicNat.eq_iff_toNat_eq).mpr h
  76  zero_step_noncollapse := by
  77    intro n h
  78    have hnat := congrArg id h
  79    simp [natOrderedRealization] at hnat
  80    exact Nat.succ_ne_zero _ hnat.symm
  81
  82/-- Order on the carrier matches the recovered Peano order. -/

depends on (11)

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