`ordered_interpret_le_iff`

proved

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module: IndisputableMonolith.Foundation.OrderedLogicRealization
domain: Foundation
line: 83 · github
papers citing: none yet

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IndisputableMonolith.Foundation.OrderedLogicRealization on GitHub at line 83.

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depends on

formal source

  80    exact Nat.succ_ne_zero _ hnat.symm
  81
  82/-- Order on the carrier matches the recovered Peano order. -/
  83theorem ordered_interpret_le_iff (a b : ArithmeticFromLogic.LogicNat) :
  84    ArithmeticFromLogic.LogicNat.toNat a ≤ ArithmeticFromLogic.LogicNat.toNat b ↔ a ≤ b := by
  85  exact (ArithmeticFromLogic.LogicNat.toNat_le a b).symm
  86
  87end OrderedLogicRealization
  88end Foundation
  89end IndisputableMonolith

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