Main Results


Theorem soundness s : prv s -> forall (M:cmodel) (w:M), eval s w.

Theorem informative_completeness s :
    prv (fImp s fF)
  + (exists2 M:fmodel, #|M| <= 2^(f_size s) & exists w:M, eval s w).

Corollary prv_dec s : decidable (prv s).

Corollary sat_dec s : decidable (exists (M:cmodel) (w:M), eval s w).

Corollary valid_dec s : decidable (forall (M:cmodel) (w:M), eval s w).

Corollary small_models s:
  (exists (M:cmodel) (w:M), eval s w) ->
  (exists2 M:fmodel, #|M| <= 2^(f_size s) & exists w:M, eval s w).

Canonicity of the pruning demo

Fact DD_canonical F (sfc_F : sf_closed F) (C : clause) :
  reflect (C \in S0 F /\ exists M : cmodel, sat M C) (C \in DD F).

Proposition support_sat C :
  (exists M, sat M C) <->
  (exists D, [/\ D \in S0 (sfc C), (exists M, sat M D) & suppC D C]).

Gentzen System

Theorem gen_completeness C : gen C + (exists M : fmodel, sat M C).

Corollary gen_correctness C : gen C <-> ~ (exists M : cmodel, sat M C).

Corollary gen_dec C : decidable (gen C).

Universal Model

Theorem UM_universal s :
  (exists (M:cmodel) (w:M), eval s w) -> (exists (w:UM), eval s w).

Soundness for all Kripke Models equivalent to XM

Theorem xm_soundness (xm : XM) s : prv s -> forall (M : ts) (w : M), eval s w.

Lemma XM_required : (forall s, prv s -> forall (M : ts) (w : M), eval s w) -> XM.