def
definition
def or abbrev
ExcludedMiddle
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formal statement (Lean)
108def ExcludedMiddle (C : ComparisonOperator) : Prop :=
proof body
Definition body.
109 ContinuousOn (Function.uncurry C) (Set.Ioi (0 : ℝ) ×ˢ Set.Ioi (0 : ℝ))
110
111/-- **Scale invariance**: the cost of a comparison depends only on the
112ratio of the two quantities. This is the structural bridge from a
113two-argument comparison operator to a one-argument cost on positive ratios.
114It is what allows the four laws of logic, which make no reference to absolute
115scale, to be expressed as constraints on the multiplicative group ℝ₊. -/
used by (14)
-
SatisfiesLawsOfLogicContinuous -
excluded_middle_implies_continuous -
non_contradiction_and_scale_imply_reciprocal -
SatisfiesLawsOfLogic -
canonical_excluded_middle -
MagnitudeOfMismatch -
OperativePositiveRatioComparison -
FiniteLogicalComparison -
truth_eval_implies_totality -
ofPositiveRatioComparison -
constZero_continuous -
SatisfiesLawsOfLogicAbsoluteFloor -
SatisfiesLawsOfLogicCanonical -
strictPositiveRatioRealization