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theorem proved term proof

involutionOp_shiftInvOp

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formal statement (Lean)

 191theorem involutionOp_shiftInvOp (p : Nat.Primes) :
 192    involutionOp ∘ₗ shiftInvOp p = shiftOp p ∘ₗ involutionOp := by

proof body

Term-mode proof.

 193  ext v
 194  simp only [LinearMap.coe_comp, Function.comp_apply,
 195             shiftInvOp_single, involutionOp_single, shiftOp_single,
 196             Finsupp.lsingle_apply]
 197  congr 1
 198  abel
 199
 200/-- The shift and inverse-shift compose to the identity (formal unitarity
 201    of `V_p`). -/

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