def
definition
def or abbrev
NonContradiction
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formal statement (Lean)
100def NonContradiction (C : ComparisonOperator) : Prop :=
proof body
Definition body.
101 ∀ x y : ℝ, 0 < x → 0 < y → C x y = C y x
102
103/-- **Excluded middle (totality and continuity)**: every comparison returns a
104definite real value and small perturbations of inputs give small
105perturbations of cost. The mathematical counterpart of the Aristotelian
106law A ∨ ¬A applied to continuous comparisons: there is no "neither" outcome
107on the comparison's domain. -/
used by (12)
-
SatisfiesLawsOfLogicContinuous -
non_contradiction_and_scale_imply_reciprocal -
SatisfiesLawsOfLogic -
canonical_non_contradiction -
MagnitudeOfMismatch -
OperativePositiveRatioComparison -
FiniteLogicalComparison -
truth_eval_implies_non_contradiction -
constZero_nonContradiction -
SatisfiesLawsOfLogicAbsoluteFloor -
SatisfiesLawsOfLogicCanonical -
equality_cost_satisfies_definitional