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theorem proved term proof

pointInterface_separates

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formal statement (Lean)

 111theorem pointInterface_separates {K : Type*} {x₀ y : K} (h : x₀ ≠ y) :
 112    Separates (pointInterface x₀) x₀ y := by

proof body

Term-mode proof.

 113  unfold Separates
 114  rw [pointInterface_at_ref x₀]
 115  have hy : y ≠ x₀ := fun h' => h h'.symm
 116  rw [pointInterface_away hy]
 117  norm_num
 118
 119/-! ## Main Theorem -/
 120
 121/-- **Observer from recognition.**
 122
 123If a carrier admits any non-trivial recognition, then there exists a finite
 124interface, hence a primitive observer, that separates a distinguished pair.
 125
 126This is the pre-physical observer theorem: observer-dependence is not added
 127at the quantum-measurement layer. It is forced at the first moment a
 128distinction becomes an event. -/

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depends on (16)

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