def
definition
def or abbrev
HasMultiplicativeConsistency
show as:
view Lean formalization →
formal statement (Lean)
72def HasMultiplicativeConsistency (F : ℝ → ℝ) : Prop :=
proof body
Definition body.
73 ∃ P : ℝ → ℝ → ℝ, ∀ x y : ℝ, 0 < x → 0 < y →
74 F (x * y) + F (x / y) = P (F x) (F y)
75
76/-! ## The Ultimate Theorem -/
77
78/-- **THEOREM (Ultimate Inevitability)**
79
80The three primitive requirements (symmetry, normalization, consistency)
81plus regularity (smoothness, calibration) uniquely determine:
821. F = J
832. P = the RCL
84
85There is no weaker foundation that still defines "cost of comparison."
86-/
used by (20)
-
axiom_bundle_necessary -
bilinear_family_forced -
F_div_swap_of_P_symmetric -
F_symmetric_of_P_symmetric -
HasMultiplicativeConsistency -
P_symmetric_from_F_symmetric -
symmetry_and_normalization_constrain_P -
gate_from_polynomial_consistency -
polynomial_consistency_forces_rcl -
polynomial_consistency_implies_right_affine -
consistency_defines_composition -
ultimate_inevitability -
laws_of_logic_imply_dalembert_hypotheses -
RCL_is_unique_functional_form_of_logic -
route_independence_implies_multiplicative_consistency -
rcl_from_canonical_mismatch_encoding -
RCLFamily -
rcl_direct_theorem -
rcl_polynomial_closure_theorem -
rcl_from_truth_evaluable_comparison