+ aux steps [] [] bag [goal]
+;;
+
+let combine_demodulation_proofs bag env goal (pl,ml,l) (pr,mr,r) =
+ let proof,m,eq,ty,left,right = open_goal goal in
+ let pl =
+ List.map
+ (fun (rule,pos,id,subst,pred) ->
+ let pred =
+ match pred with
+ | Cic.Lambda (name,src,tgt) ->
+ Cic.Lambda (name,src,
+ Cic.Appl[eq;ty;tgt;CicSubstitution.lift 1 right])
+ | _ -> assert false
+ in
+ rule,pos,id,subst,pred)
+ pl
+ in
+ let pr =
+ List.map
+ (fun (rule,pos,id,subst,pred) ->
+ let pred =
+ match pred with
+ | Cic.Lambda (name,src,tgt) ->
+ Cic.Lambda (name,src,
+ Cic.Appl[eq;ty;CicSubstitution.lift 1 l;tgt])
+ | _ -> assert false
+ in
+ rule,pos,id,subst,pred)
+ pr
+ in
+ (pr@pl@proof, m, Cic.Appl [eq;ty;l;r])
+;;
+
+let demodulation_all_goal bag env table goal maxnf =
+ let proof,menv,eq,ty,left,right = open_goal goal in
+ let v1, bag, l_demod = demod_all maxnf bag env table ([],menv,left) in
+ let v2, bag, r_demod = demod_all maxnf bag env table ([],menv,right) in
+ let l_demod = if l_demod = [] then [ [], menv, left ] else l_demod in
+ let r_demod = if r_demod = [] then [ [], menv, right ] else r_demod in
+ List.fold_left
+ (fun acc (_,_,l as ld) ->
+ List.fold_left
+ (fun acc (_,_,r as rd) ->
+ combine_demodulation_proofs bag env goal ld rd :: acc)
+ acc r_demod)
+ [] l_demod
+;;
+
+let solve_demodulating bag env table initgoal steps =
+ let proof,menv,eq,ty,left,right = open_goal initgoal in
+ let uri =
+ match eq with
+ | Cic.MutInd (u,_,_) -> u
+ | _ -> assert false