Module Cc_plugin.Ccproof

type rule =
| Ax of Ccalgo.axiom

if ⊢ t = u :: A, then ⊢ t = u :: A

| SymAx of Ccalgo.axiom

if ⊢ t = u : A, then ⊢ u = t :: A

| Refl of Ccalgo.ATerm.t
| Trans of proof * proof

⊢ t = u :: A -> ⊢ u = v :: A -> ⊢ t = v :: A

| Congr of proof * proof

⊢ f = g :: forall x : A, B -> ⊢ t = u :: A -> f t = g u :: Bt Assumes that Bt ≡ Bu for this to make sense!

| Inject of proof * Constr.pconstructor * int * int

⊢ ci v = ci w :: Ind(args) -> ⊢ v = w :: T where T is the type of the n-th argument of ci, assuming they coincide

and proof = private {
p_lhs : Ccalgo.ATerm.t;
p_rhs : Ccalgo.ATerm.t;
p_rule : rule;
}
val build_proof : Environ.env -> Evd.evar_map -> Ccalgo.forest -> [ `Discr of int * Ccalgo.pa_constructor * int * Ccalgo.pa_constructor | `Prove of int * int ] -> proof