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|
open GenericLib
let set_singleton (c : coq_expr) : coq_expr = gApp (gInject "set1") [c]
let set_empty : coq_expr = gInject "set0"
let set_full : coq_expr = gInject "setT"
let set_bigcup (x : string) (p : coq_expr) (c : var -> coq_expr) : coq_expr =
gApp (gInject "bigcup") [p; gFun [x] (fun [x] -> c x)]
let set_suchThat (x : string) (t : coq_expr) (p : var -> coq_expr) : coq_expr =
gFunTyped [("x", t)] (fun [x] -> p x)
let set_eq c1 c2 = gApp (gInject "set_eq") [c1;c2]
let set_incl c1 c2 = gApp (gInject "set_incl") [c1;c2]
let set_union c1 c2 = gApp (gInject "setU") [c1;c2]
let set_int c1 c2 = gApp (gInject "setI") [c1;c2]
let imset f s =
gApp (gInject "imset") [f; s]
let sub0set =
gApp ~explicit:true (gInject "sub0set") [hole; hole]
let imset_set0_subset =
gApp ~explicit:true (gInject "imset_set0_subset") [hole; hole; hole; hole]
let rec set_unions = function
| [] -> failwith "empty set unions"
| [x] -> x
| x::xs -> set_union x (set_unions xs)
let set_eq_refl x =
gApp (gInject "set_eq_refl") [x]
let set_incl_refl =
gApp ~explicit:true (gInject "subset_refl") [hole; hole]
let _incl_subset l1 l2 p =
gApp (gInject "incl_subset") [l1; l2; p]
let incl_refl =
gApp (gInject "incl_refl") [hole]
let incl_hd_same p =
gApp ~explicit:true (gInject "incl_hd_same") [hole; hole; hole; hole; p]
let incl_tl p =
gApp (gInject "incl_tl") [hole; p]
let setU_set_eq_compat x1 x2 =
gApp (gInject "setU_set_eq_compat") [x1; x2]
let setU_set0_r x1 x2 =
gApp (gInject "setU_set0_r") [x1; x2]
let set_eq_trans x1 x2 =
gApp (gInject "set_eq_trans") [x1; x2]
let set_incl_trans x1 x2 =
gApp (gInject "subset_trans") [x1; x2]
let setU_set0_l x1 x2 =
gApp (gInject "setU_set0_l") [x1; x2]
let setU_set0_neut_eq x1 x2 =
gApp (gInject "setU_set0_neut_eq") [x1; x2]
let eq_bigcupl x1 x2 p = gApp (gInject "eq_bigcupl") [x1; x2; p]
let cons_set_eq x l = gApp (gInject "cons_set_eq") [x; l]
let singl_set_eq a x = gApp ~explicit:true (gInject "singl_set_eq") [a; x]
let bigcup_setU_l x1 x2 x3 = gApp (gInject "bigcup_setU_l") [x1; x2; x3]
let bigcup_set1 x1 x2 = gApp (gInject "bigcup_set1") [x1 ; x2]
let subset_respects_set_eq_l p1 p2 =
gApp (gInject "subset_respects_set_eq_l") [p1; p2]
let subset_respects_set_eq_r p1 p2 =
gApp (gInject "subset_respects_set_eq_r") [p1; p2]
let subset_respects_set_eq p1 p2 p3 =
gApp ~explicit:true (gInject "subset_respects_set_eq")
[hole; hole; hole; hole; hole; p1; p2; p3]
(* maybe add a new lemma? *)
let subset_set_eq_compat p1 p2 p3 =
gApp (gInject "subset_respects_set_eq") [p1; p2; p3]
let incl_bigcupl p =
gApp (gInject "incl_bigcupl") [p]
let incl_bigcup_compat p1 p2 =
gApp (gInject "incl_bigcup_compat") [p1; p2]
let imset_isSome s =
gApp ~explicit:true (gInject "imset_isSome") [hole; s]
let isSomeSet a =
gFun ["x"]
(fun [x] ->
gApp (gInject "is_true")
[gApp ~explicit:true (gInject "isSome") [a; gVar x]]
)
[@ocaml.warning "-8"]
let incl_subset l1 l2 p =
gApp ~explicit:true (gInject "incl_subset") [hole; l1; l2; p]
let setU_set_subset_compat p1 p2 =
gApp (gInject "setU_set_subset_compat") [p1; p2]
let setI_subset_compat p1 p2 =
gApp ~explicit:true (gInject "setI_subset_compat")
[hole; hole; hole; hole; hole; p1; p2]
let nil_subset p =
gApp (gInject "nil_subset") [p]
let cons_subset (hd : coq_expr) (tl : coq_expr) (p : coq_expr) (phd : coq_expr) (ptl : coq_expr) =
gApp ~explicit:true (gInject "cons_subset") [hole; hd; tl; p; phd; ptl]
let setI_set_incl hsub1 hsub2 =
gApp ~explicit:true (gInject "setI_set_incl") [hole; hole; hole; hole; hsub1; hsub2]
let setI_set_eq_r p =
gApp ~explicit:true (gInject "setI_set_eq_r") [hole; hole; hole; hole; p]
let setU_subset_r s2 p =
gApp ~explicit:true (gInject "setU_subset_r") [hole; hole; s2; hole; p]
let setU_subset_l s2 p =
gApp ~explicit:true (gInject "setU_subset_l") [hole; hole; s2; hole; p]
let imset_set0_incl f x h =
gApp ~explicit:true (gInject "imset_set0_incl") [hole; hole; f; x; h]
let imset_singl_incl x f y h =
gApp ~explicit:true (gInject "imset_singl_incl") [hole; hole; x; f; y; h]
let imset_union_incl s1 s2 f x hin =
gApp ~explicit:true (gInject "imset_union_incl") [hole; hole; s1; s2; f; x; hin]
let imset_incl h =
gApp (gInject "imset_incl") [h]
let rewrite_set_r seq p =
gApp ~explicit:true (gInject "rewrite_set_r") [hole; hole; hole; hole; p; seq]
let rewrite_set_l seq p =
gApp ~explicit:true (gInject "rewrite_set_l") [hole; hole; hole; hole; p; seq]
let imset_bigcup_incl_l f a g x h =
gApp ~explicit:true
(gInject "imset_bigcup_incl_l")
[hole; hole; hole; f; a; g; x; h]
let set_eq_set_incl_r heq =
gApp ~explicit:true (gInject "set_eq_set_incl_r") [hole; hole; hole; heq]
let set_eq_set_incl_l heq =
gApp ~explicit:true (gInject "set_eq_set_incl_l") [hole; hole; hole; heq]
let in_imset f s x hin =
gApp ~explicit:true (gInject "in_imset") [hole; hole; f; s; x; hin]
let lift_union_compat h1 h2 =
gApp
~explicit:true (gInject "union_lift_subset_compat")
[hole; hole; hole; hole; hole; h1; h2]
let lift_subset_pres_r h =
gApp
~explicit:true (gInject "lift_subset_pres_r")
[hole; hole; hole; hole; h]
let lift_subset_pres_l h =
gApp
~explicit:true (gInject "lift_subset_pres_l")
[hole; hole; hole; hole; h]
let bigcup_set0_subset f s =
gApp
~explicit:true (gInject "bigcup_set0_subset")
[hole; hole; f; s]
let bigcup_set_U h1 h2 =
gApp
~explicit:true (gInject "bigcup_set_U")
[hole; hole; hole; hole; hole; hole; h1; h2]
let bigcup_set_I_l h =
gApp
~explicit:true (gInject "bigcup_set_I_l")
[hole; hole; hole; hole; hole; hole; h]
let set_incl_setI_l h =
gApp
~explicit:true (gInject "set_incl_setI_l")
[hole; hole; hole; hole; h]
let set_incl_setI_r h =
gApp
~explicit:true (gInject "set_incl_setI_r")
[hole; hole; hole; hole; h]
let set_incl_setU_l h1 h2 =
gApp
~explicit:true (gInject "set_incl_setU_l")
[hole; hole; hole; hole; h1; h2]
let bigcup_cons_subset a b h1 h2 =
gApp
~explicit:true (gInject "bigcup_cons_subset")
[a; b; hole; hole; hole; hole; h1; h2]
let bigcup_cons_subset_r a b h1 h2 =
gApp
~explicit:true (gInject "bigcup_cons_subset_r")
[a; b; hole; hole; hole; hole; hole; h1; h2]
let bigcup_setI_cons_subset_r a b h1 h2 h3 =
gApp
~explicit:true (gInject "bigcup_setI_cons_subset_r")
[a; b; hole;
hole; hole; hole; hole; hole; h1; h2; h3]
let imset_bigcup_setI_cons_subset_r a b h1 h2 h3 =
gApp
~explicit:true (gInject "imset_bigcup_setI_cons_subset_r")
[a; b; hole; hole; hole; hole; hole; hole; h1; h2; h3]
let bigcup_nil_subset =
gApp
~explicit:true (gInject "bigcup_nil_subset")
[hole; hole; hole; hole]
let isSome_subset p =
gApp
~explicit:true (gInject "isSome_subset")
[hole; hole; hole; hole; hole; p]
(* let bigcup_cons_setI_subset_compat a f h1 h2 = *)
(* gApp *)
(* ~explicit:true (gInject "bigcup_cons_setI_subset_compat") *)
(* [a; hole; f; hole; hole; hole; hole; hole; h1; h2] *)
let bigcup_cons_setI_subset_pres a f h =
gApp
~explicit:true (gInject "bigcup_cons_setI_subset_pres")
[a; hole; f; hole; hole; hole; hole; h]
let bigcup_cons_setI_subset_compat_backtrack h1 h2 =
gApp
~explicit:true (gInject "bigcup_cons_setI_subset_compat_backtrack")
[hole; hole; hole; hole; hole; hole; hole; h1; h2]
let bigcup_cons_setI_subset_compat_backtrack_weak h1 h2 =
gApp
~explicit:true (gInject "bigcup_cons_setI_subset_compat_backtrack_weak")
[hole; hole; hole; hole; hole; hole; h1; h2]
let bigcup_cons_setI_subset_pres_backtrack h =
gApp
~explicit:true (gInject "bigcup_cons_setI_subset_pres_backtrack")
[hole; hole; hole; hole; hole; hole; h]
let bigcup_cons_setI_subset_pres_backtrack_weak h =
gApp
~explicit:true (gInject "bigcup_cons_setI_subset_pres_backtrack_weak")
[hole; hole; hole; hole; hole; h]
let bigcup_nil_setI f l s =
gApp
~explicit:true (gInject "bigcup_nil_setI")
[hole; hole; f; l; s]
let isSome_set_eq h1 h2 =
gApp
~explicit:true (gInject "isSome_set_eq")
[hole; hole; hole; h1; h2]
let set_eq_isSome_sound h =
gApp
~explicit:true (gInject "set_eq_isSome_sound")
[hole; hole; hole; h]
let set_eq_isSome_complete h =
gApp
~explicit:true (gInject "set_eq_isSome_complete")
[hole; hole; hole; h]
|
