theorem
proved
term proof
boson_symmetric_wavefunction
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formal statement (Lean)
201theorem boson_symmetric_wavefunction (s : Spin) (h : s.isInteger) :
202 exchangeSymmetryFromSpin s = ExchangeSymmetry.symmetric := by
proof body
Term-mode proof.
203 simp [exchangeSymmetryFromSpin]
204 intro h'
205 exact absurd (And.intro h h') (Spin.int_half_exclusive s)
206
207/-! ## Pauli Exclusion Principle -/
208
209/-- **THEOREM (Pauli Exclusion)**: Fermions cannot occupy the same quantum state.
210
211 This follows from antisymmetry: if two fermions are in the same state,
212 the wavefunction ψ(1,1) = -ψ(1,1), which implies ψ(1,1) = 0.
213
214 Proof: From x = -x, add x to both sides: 2x = 0. Since char(ℂ) = 0, we have x = 0. -/