Definition xnnormalise (t : Formula Z) : NFormula Z :=
let (lhs,o,rhs) := t in
let lhs := normZ lhs in
let rhs := normZ rhs in
match o with
| OpEq  => (psub rhs lhs,  Equal)
| OpNEq => (psub rhs lhs,  NonEqual)
| OpGt  => (psub lhs rhs,  Strict)
| OpLt  => (psub rhs lhs,  Strict)
| OpGe  => (psub lhs rhs,  NonStrict)
| OpLe =>  (psub rhs lhs,  NonStrict)
end.

Lemma xnnormalise_correct :
forall env f,
eval_nformula env (xnnormalise f) <-> Zeval_formula env Tauto.isProp f.