pith. machine review for the scientific record. sign in
def definition def or abbrev

NonContradiction

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

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)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (19)

Lean names referenced from this declaration's body.