`continuous_composition_not_enough`

proved

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module: IndisputableMonolith.Foundation.LogicAsFunctionalEquation.FiniteLogicalComparison
domain: Foundation
line: 90 · github
papers citing: none yet

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IndisputableMonolith.Foundation.LogicAsFunctionalEquation.FiniteLogicalComparison on GitHub at line 90.

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formal source

  87
  88/-- Searchable boundary theorem: arbitrary continuous composition is not enough
  89to force the RCL family. -/
  90theorem continuous_composition_not_enough :
  91    ¬ ∃ c : ℝ, ∀ a b : ℝ, 0 < a → 0 < b →
  92      quarticCombiner a b = 2 * a + 2 * b + c * a * b :=
  93  quarticCombiner_not_rcl_family
  94
  95/-- Searchable boundary theorem: analytic composition is not enough to force
  96degree-two RCL form. -/
  97theorem analytic_composition_not_enough :
  98    ¬ ∃ c : ℝ, ∀ s : ℝ, reparamDiagonal s = degreeTwoDiagonal c s :=
  99  reparam_diagonal_not_degree_two
 100
 101end LogicAsFunctionalEquation
 102end Foundation
 103end IndisputableMonolith

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