def
definition
def or abbrev
Identity
show as:
view Lean formalization →
formal statement (Lean)
93def Identity (C : ComparisonOperator) : Prop :=
proof body
Definition body.
94 ∀ x : ℝ, 0 < x → C x x = 0
95
96/-- **Non-contradiction (reciprocal symmetry)**: the cost of comparing x to y
97equals the cost of comparing y to x. The mathematical counterpart of the
98Aristotelian law ¬(A ∧ ¬A): if comparison were not single-valued under
99reordering, the same comparison would simultaneously hold and not hold. -/
used by (40)
-
windowSums_shift_equivariant -
canonicalLedgerAlgObj -
canonicalOctaveAlgObj -
CostAlgHomKappa -
CostAlgPlusHom -
LayerSysPlusHom -
monotone_preserves_argmin -
PhiRingHom -
qualiaDomain -
recAlg_comp_assoc -
RecAlgHom -
recAlg_id_left -
shell -
tau0_pos -
Jlog_unit_curvature -
normalized_implies_G_zero -
extraction_cost_strict_minimum -
extractionSystemCost -
Hom -
axiom_bundle_transcendental -
cosh_log_eq_jcost_rpow -
CostAlpha -
derivedCostOn -
SatisfiesLawsOfLogicContinuous -
derivedCost -
identity_implies_normalized -
SatisfiesLawsOfLogic -
canonical_identity -
MagnitudeOfMismatch -
OperativePositiveRatioComparison