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structure definition def or abbrev

LogicSupported

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formal statement (Lean)

  97structure LogicSupported (K : Type*) [Mul K] [Zero K] [One K] [LT K] where
  98  zero_lt_one_in_K : (0 : K) < 1
  99  C : ComparisonOperatorOn K
 100  identity : IdentityOn C
 101  non_contradiction : NonContradictionOn C
 102  scale_invariant : ScaleInvariantOn C
 103  distinguishability : DistinguishabilityOn C
 104
 105/-- **Bootstrap theorem (named-hypothesis form)**: a linearly ordered
 106field on which the Law of Logic is supported and which is Archimedean
 107and conditionally complete is canonically isomorphic to `ℝ` as an
 108ordered field. The Archimedean and conditional-completeness
 109hypotheses are the analytic content the Law of Logic does not on its
 110own provide; they are named here as inputs.
 111
 112The conclusion is the existence of an order-preserving ring
 113isomorphism with `ℝ`. -/

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