whileConvPSemSound : {l : Level} → (input : Envc) → ((vari input ≡ 0) ∧ (varn input ≡ c)) implies (varn input + vari input ≡ c10 input)
whileConvPSemSound input = proof λ x → (conversion input x) where
  conversion : (env : Envc ) → (vari env ≡ 0) /\ (varn env ≡ c10 env) → varn env + vari env ≡ c10 env
  conversion e record { pi1 = refl ; pi2 = refl } = +zero