149theorem frequentist_vindicated (obs : Observer) (x : ℝ) : 150 -- The projection is deterministic: same input → same output 151 ∀ y : ℝ, x = y → project obs x = project obs y := by
proof body
Term-mode proof.
152 intro y hxy 153 rw [hxy] 154 155/-- **Theorem (Bayesian Vindicated)**: 156 The Bayesian insight is correct: probability is about information states. 157 158 Formalization: For any two observers with DIFFERENT resolutions, there 159 exists a state x such that the two observers project x to DIFFERENT outcomes. 160 This means their "probability assignments" differ — probability depends on 161 the observer's information state (resolution), not just on reality. 162 163 This is the formal content of Bayesian subjectivism: same underlying state, 164 different probabilities, because different observers have different resolutions. -/
depends on (17)
Lean names referenced from this declaration's body.