package coq

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package coq
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Proof format used by the proof-generating procedures. It is fairly close to Coq format but a bit more liberal.

It is used for proofs over Z, Q, R. However, certain constructions e.g. CutPrf are only relevant for Z.

type prf_rule =
  1. | Annot of string * prf_rule
  2. | Hyp of int
  3. | Def of int
  4. | Ref of int
  5. | Cst of NumCompat.Q.t
  6. | Zero
  7. | Square of Vect.t
  8. | MulC of Vect.t * prf_rule
  9. | Gcd of NumCompat.Z.t * prf_rule
  10. | MulPrf of prf_rule * prf_rule
  11. | AddPrf of prf_rule * prf_rule
  12. | CutPrf of prf_rule
  13. | LetPrf of prf_rule * prf_rule
type proof =
  1. | Done
  2. | Step of int * prf_rule * proof
  3. | Split of int * Vect.t * proof * proof
  4. | Enum of int * prf_rule * Vect.t * prf_rule * proof list
  5. | ExProof of int * int * int * var * var * var * proof
val pr_size : prf_rule -> NumCompat.Q.t
val pr_rule_max_def : prf_rule -> int
val pr_rule_max_hyp : prf_rule -> int
val proof_max_def : proof -> int
val normalise_proof : int -> proof -> int * proof
val output_prf_rule : out_channel -> prf_rule -> unit
val output_proof : out_channel -> proof -> unit
val add_proof : prf_rule -> prf_rule -> prf_rule
val mul_cst_proof : NumCompat.Q.t -> prf_rule -> prf_rule
val mul_proof : prf_rule -> prf_rule -> prf_rule
val compile_proof : int list -> proof -> Micromega.zArithProof
module Env : sig ... end
val cmpl_prf_rule : ('a Micromega.pExpr -> 'a Micromega.pol) -> (NumCompat.Q.t -> 'a) -> Env.t -> prf_rule -> 'a Micromega.psatz
val proof_of_farkas : prf_rule Mutils.IMap.t -> Vect.t -> prf_rule
val eval_prf_rule : (int -> LinPoly.t * op) -> prf_rule -> LinPoly.t * op
val eval_proof : (LinPoly.t * op) Mutils.IMap.t -> proof -> bool
val simplify_proof : proof -> proof * Mutils.ISet.t
module PrfRuleMap : Map.S with type key = prf_rule