def
definition
def or abbrev
HasMultiplicativeConsistency
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formal statement (Lean)
72def HasMultiplicativeConsistency (F : ℝ → ℝ) (P : ℝ → ℝ → ℝ) : Prop :=
proof body
Definition body.
73 ∀ x y : ℝ, 0 < x → 0 < y → F (x * y) + F (x / y) = P (F x) (F y)
74
75/-! ## Derived Reciprocity (P-symmetry ⇒ F(x) = F(1/x)) -/
76
77/-- If the combiner `P` is symmetric and `F` is multiplicatively consistent with `P`,
78then `F(x/y) = F(y/x)` for all `x,y>0`. -/
used by (20)
-
axiom_bundle_necessary -
bilinear_family_forced -
F_div_swap_of_P_symmetric -
F_symmetric_of_P_symmetric -
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 -
HasMultiplicativeConsistency -
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