let start, stop = HExtlib.loc_of_floc floc in
let start_bytes = Glib.Utf8.offset_to_pos s ~pos:0 ~off:start in
let stop_bytes = Glib.Utf8.offset_to_pos s ~pos:0 ~off:stop in
- assert(stop_bytes >= start_bytes);
+ if (stop_bytes < start_bytes) then
+ Printf.sprintf "ERROR (%d > %d)" start_bytes stop_bytes, 0
+ else
let bytes = stop_bytes - start_bytes in
try
String.sub s start_bytes bytes, bytes
with Invalid_argument _ ->
- Printf.eprintf "%s/%d/%d\n" s start_bytes bytes;
- assert false
-
+ Printf.sprintf "ERROR (%s/%d/%d)" s start_bytes bytes, 0
let utf8_string_length s =
if BuildTimeConf.debug then
op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
}.
+unification hint 0 ≔
+ A : ? ⊢ carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
+
+(*
ncoercion mcarr' : ∀A. ∀M: magma A. carr1 (qpowerclass_setoid (mtcarr A))
≝ λA.λM: magma A.mcarr ? M
on _M: magma ? to carr1 (qpowerclass_setoid (mtcarr ?)).
+*)
nrecord magma_morphism_type (A,B: magma_type) : Type[0] ≝
{ mmcarr:> unary_morphism A B;
-logic/cprop.ma sets/setoids1.ma
+logic/cprop.ma hints_declaration.ma sets/setoids1.ma
sets/sets.ma logic/connectives.ma logic/cprop.ma properties/relations1.ma sets/setoids1.ma
topology/igft.ma logic/connectives.ma
datatypes/bool.ma logic/pts.ma
nat/nat.ma logic/equality.ma sets/setoids.ma
properties/relations.ma logic/pts.ma
nat/compare.ma datatypes/bool.ma nat/order.ma
+hints_declaration.ma logic/pts.ma
logic/pts.ma
nat/order.ma nat/nat.ma sets/sets.ma
algebra/unital_magmas.ma algebra/magmas.ma
digraph g {
"logic/cprop.ma" [];
+ "logic/cprop.ma" -> "hints_declaration.ma" [];
"logic/cprop.ma" -> "sets/setoids1.ma" [];
"sets/sets.ma" [];
"sets/sets.ma" -> "logic/connectives.ma" [];
"nat/compare.ma" [];
"nat/compare.ma" -> "datatypes/bool.ma" [];
"nat/compare.ma" -> "nat/order.ma" [];
+ "hints_declaration.ma" [];
+ "hints_declaration.ma" -> "logic/pts.ma" [];
"logic/pts.ma" [];
"nat/order.ma" [];
"nat/order.ma" -> "nat/nat.ma" [];
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "logic/pts.ma".
+ndefinition hint_declaration_Type0 ≝ λA:Type[0] .λa,b:A.a.
+ndefinition hint_declaration_Type1 ≝ λA:Type[1].λa,b:A.a.
+ndefinition hint_declaration_Type2 ≝ λa,b:Type[1].a.
+ndefinition hint_declaration_CProp0 ≝ λA:CProp[0].λa,b:A.a.
+ndefinition hint_declaration_CProp1 ≝ λA:CProp[1].λa,b:A.a.
+ndefinition hint_declaration_CProp2 ≝ λa,b:CProp[1].a.
+
+notation > "≔ (list0 (ident x : T )sep ,) ⊢ term 19 Px ≡ term 19 Py"
+ with precedence 90
+ for @{ ${ fold right @{'hint_decl $Px $Py} rec acc @{ ∀${ident x}:$T.$acc } } }.
+
+interpretation "hint_decl_Type2" 'hint_decl a b = (hint_declaration_Type2 a b).
+interpretation "hint_decl_CProp2" 'hint_decl a b = (hint_declaration_CProp2 a b).
+interpretation "hint_decl_Type1" 'hint_decl a b = (hint_declaration_Type1 ? a b).
+interpretation "hint_decl_CProp1" 'hint_decl a b = (hint_declaration_CProp1 ? a b).
+interpretation "hint_decl_CProp0" 'hint_decl a b = (hint_declaration_CProp0 ? a b).
+interpretation "hint_decl_Type0" 'hint_decl a b = (hint_declaration_Type0 ? a b).
(* *)
(**************************************************************************)
+include "hints_declaration.ma".
include "sets/setoids1.ma".
ndefinition CPROP: setoid1.
[ napply (H3 (H1 w)) | napply (H2 (H4 w))]##]##]
nqed.
-unification hint 0 ((λx,y.True) (carr1 CPROP) CProp[0]).
+alias symbol "hint_decl" = "hint_decl_CProp2".
+unification hint 0 ≔ ⊢ CProp[0] ≡ carr1 CPROP.
(*ndefinition CProp0_of_CPROP: carr1 CPROP → CProp[0] ≝ λx.x.
ncoercion CProp0_of_CPROP : ∀x: carr1 CPROP. CProp[0] ≝ CProp0_of_CPROP
(* *)
(**************************************************************************)
+include "hints_declaration.ma".
include "logic/equality.ma".
include "sets/setoids.ma".
napply mk_setoid [ napply nat | napply EQ]
nqed.
-unification hint 0 ((λx,y.True) (carr NAT) nat).
+alias symbol "hint_decl" = "hint_decl_Type1".
+unification hint 0 ≔ ⊢ carr NAT ≡ nat.
include "nat/minus.ma".
include "datatypes/pairs.ma".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
+
alias symbol "eq" = "setoid eq".
alias symbol "eq" = "setoid1 eq".
alias symbol "eq" = "setoid eq".
[##2: napply ad_hoc9; nassumption] *; *; #Hrec1; #Hrec2; #Hrec3; napply conj
[##2: nassumption
|napply conj
- [napply (eq_rect_CProp0_r ?? (λx.λ_. m = x + snd … (iso_nat_nat_union s (m - s (S n')) n')) ??
- (split_big_plus
- (S n' - fst … (iso_nat_nat_union s (m - s (S n')) n'))
- (n' - fst … (iso_nat_nat_union s (m - s (S n')) n'))
- (λi.λ_.s (S (i + fst … (iso_nat_nat_union s (m - s (S n')) n'))))?))
- [##2: napply ad_hoc11]
- napply (eq_rect_CProp0_r ?? (λx.λ_. ? = ? + big_plus x (λ_.λ_:? < x.?) + ?)
- ?? (ad_hoc12 n' (fst … (iso_nat_nat_union s (m - s (S n')) n')) ?))
- [##2: nassumption]
- nwhd in ⊢ (???(?(??%)?));
- nrewrite > (ad_hoc13 n' (fst … (iso_nat_nat_union s (m - s (S n')) n')) ?)
- [##2: nassumption]
+ [nrewrite > (split_big_plus …); ##[##2:napply ad_hoc11;##|##3:##skip]
+ nrewrite > (ad_hoc12 …); ##[##2: nassumption]
+ nwhd in ⊢ (????(?(??%)?));
+ nrewrite > (ad_hoc13 …);##[##2: nassumption]
napply ad_hoc14 [ napply not_lt_to_le; nassumption ]
nwhd in ⊢ (???(?(??%)?));
- napply (eq_rect_CProp0_r ?? (λx.λ_. ? = x + ?) ??
- (plus_n_O (big_plus (n' - fst … (iso_nat_nat_union s (m - s (S n')) n'))
- (λi.λ_.s (S (i + fst … (iso_nat_nat_union s (m - s (S n')) n')))))));
- nassumption
- | napply le_S; nassumption ]##]##]##]
+ nrewrite > (plus_n_O …);
+ nassumption;
+ ##| napply le_S; nassumption ]##]##]##]
nqed.
ntheorem iso_nat_nat_union_pre:
nrewrite > (split_big_plus (S n) (S i1) (λi.λ_.s i) ?)
[##2: napply le_to_le_S_S; nassumption]
napply ad_hoc15
- [ nrewrite > (minus_S_S n i1 …); napply big_plus_preserves_ext; #i; #_;
+ [ nwhd in ⊢ (???(?%?));
+
+ napply (eq_rect_CProp0_r nat (n - i1) (λx.λy.?) ?? (minus_S_S …)); STOP
+
+ nrewrite > (minus_S_S n i1); napply big_plus_preserves_ext; #i; #_;
nrewrite > (plus_n_S i i1); napply refl
| nrewrite > (split_big_plus (S i1) i1 (λi.λ_.s i) ?) [##2: napply le_S; napply le_n]
napply ad_hoc16; nrewrite > (minus_S i1); nnormalize; nrewrite > (plus_n_O (s i1) …);
∀f:isomorphism ?? (Nat_ n) (indexes ? P).
(∀i. isomorphism ?? (Nat_ (s i)) (class ? P (iso_f ???? f i))) →
(isomorphism ?? (Nat_ (big_plus n (λi.λ_.s i))) (Full_set A)).
- #A; #P; #Sn; ncases Sn
+ STOP #A; #P; #Sn; ncases Sn
[ #s; #f; #fi;
ngeneralize in match (covers ? P) in ⊢ ?; *; #_; #H;
(*
+
(**************************************************************************)
(* ___ *)
(* ||M|| *)
ndefinition big_intersection ≝ λA,B.λT:Ω \sup A.λf:A → Ω \sup B.{ x | ∀i. i ∈ T → x ∈ f i }.
ndefinition full_set: ∀A. Ω \sup A ≝ λA.{ x | True }.
-(* bug dichiarazione coercion qui *)
-(* ncoercion full_set : ∀A:Type[0]. Ω \sup A ≝ full_set on _A: Type[0] to (Ω \sup ?). *)
+ncoercion full_set : ∀A:Type[0]. Ω \sup A ≝ full_set on A: Type[0] to (Ω \sup ?).
nlemma subseteq_refl: ∀A.∀S: Ω \sup A. S ⊆ S.
#A; #S; #x; #H; nassumption.
| napply seteq ]
nqed.
-unification hint 0 (∀A. (λx,y.True) (carr1 (powerclass_setoid A)) (Ω \sup A)).
+include "hints_declaration.ma".
+
+alias symbol "hint_decl" = "hint_decl_Type2".
+unification hint 0 ≔ A : ? ⊢ carr1 (powerclass_setoid A) ≡ Ω^A.
(************ SETS OVER SETOIDS ********************)
include "logic/cprop.ma".
nrecord qpowerclass (A: setoid) : Type[1] ≝
- { pc:> Ω \sup A;
+ { pc:> Ω^A;
mem_ok': ∀x,x':A. x=x' → (x ∈ pc) = (x' ∈ pc)
}.
ndefinition Full_set: ∀A. qpowerclass A.
#A; napply mk_qpowerclass
[ napply (full_set A)
- | #x; #x'; #H; nnormalize in ⊢ (?%?%%); (* bug universi qui napply refl1;*)
- napply mk_iff; #K; nassumption ]
+ | #x; #x'; #H; napply refl1; ##]
nqed.
ndefinition qseteq: ∀A. equivalence_relation1 (qpowerclass A).
#A; napply mk_equivalence_relation1
- [ napply (λS,S':qpowerclass A. eq_rel1 ? (eq1 (powerclass_setoid A)) S S')
+ [ napply (λS,S':qpowerclass A. S = S')
| #S; napply (refl1 ? (seteq A))
| #S; #S'; napply (sym1 ? (seteq A))
| #S; #T; #U; napply (trans1 ? (seteq A))]
| napply (qseteq A) ]
nqed.
-unification hint 0 (∀A. (λx,y.True) (carr1 (qpowerclass_setoid A)) (qpowerclass A)).
-ncoercion qpowerclass_hint: ∀A: setoid. ∀S: qpowerclass_setoid A. Ω \sup A ≝ λA.λS.S
- on _S: (carr1 (qpowerclass_setoid ?)) to (Ω \sup ?).
+unification hint 0 ≔ A : ? ⊢ carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
nlemma mem_ok: ∀A. binary_morphism1 (setoid1_of_setoid A) (qpowerclass_setoid A) CPROP.
#A; napply mk_binary_morphism1
- [ napply (λx.λS: qpowerclass_setoid A. x ∈ S) (* CSC: ??? *)
- | #a; #a'; #b; #b'; #Ha; #Hb; (* CSC: qui *; non funziona *)
- nwhd; nwhd in ⊢ (? (? % ??) (? % ??)); napply mk_iff; #H
- [ ncases Hb; #Hb1; #_; napply Hb1; napply (. (mem_ok' …))
- [ nassumption | napply Ha^-1 | ##skip ]
- ##| ncases Hb; #_; #Hb2; napply Hb2; napply (. (mem_ok' …))
- [ nassumption | napply Ha | ##skip ]##]
+ [ #x; napply (λS: qpowerclass_setoid ?. x ∈ S) (* ERROR CSC: ??? *)
+ | #a; #a'; #b; #b'; #Ha; *; #Hb1; #Hb2; napply mk_iff; #H;
+ ##[ napply Hb1; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha^-1;##]
+ ##| napply Hb2; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha;##]
+ ##]
+ ##]
nqed.
-unification hint 0 (∀A,x,S. (λx,y.True) (fun21 ??? (mem_ok A) x S) (mem A S x)).
+unification hint 0 ≔
+ A : setoid, x : ?, S : ? ⊢ (mem_ok A) x S ≡ mem A S x.
nlemma subseteq_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) CPROP.
#A; napply mk_binary_morphism1
[ napply (λS,S': qpowerclass_setoid ?. S ⊆ S')
| #a; #a'; #b; #b'; *; #Ha1; #Ha2; *; #Hb1; #Hb2; napply mk_iff; #H
- [ napply (subseteq_trans … a' a) (* anche qui, perche' serve a'? *)
- [ nassumption | napply (subseteq_trans … a b); nassumption ]
- ##| napply (subseteq_trans … a a') (* anche qui, perche' serve a'? *)
- [ nassumption | napply (subseteq_trans … a' b'); nassumption ] ##]
+ [ napply (subseteq_trans … a)
+ [ nassumption | napply (subseteq_trans … b); nassumption ]
+ ##| napply (subseteq_trans … a')
+ [ nassumption | napply (subseteq_trans … b'); nassumption ] ##]
nqed.
nlemma intersect_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) (qpowerclass_setoid A).
[ #S; #S'; napply mk_qpowerclass
[ napply (S ∩ S')
| #a; #a'; #Ha; nwhd in ⊢ (? ? ? % %); napply mk_iff; *; #H1; #H2; napply conj
- [##1,2: napply (. (mem_ok' …)^-1) [##3,6: nassumption |##1,4: nassumption |##*: ##skip]
- ##|##3,4: napply (. (mem_ok' …)) [##2,5: nassumption |##1,4: nassumption |##*: ##skip]##]##]
+ [##1,2: napply (. (mem_ok' …)^-1) [##3,6: nassumption |##2,5: nassumption |##*: ##skip]
+ ##|##3,4: napply (. (mem_ok' …)) [##1,3,4,6: nassumption |##*: ##skip]##]##]
##| #a; #a'; #b; #b'; #Ha; #Hb; nwhd; napply conj; #x; nwhd in ⊢ (% → %); #H
[ napply (. ((#‡Ha^-1)‡(#‡Hb^-1))); nassumption
| napply (. ((#‡Ha)‡(#‡Hb))); nassumption ]##]
nqed.
-unification hint 0 (∀A.∀U,V.(λx,y.True) (fun21 ??? (intersect_ok A) U V) (intersect A U V)).
+(*
+unification hint 0 ≔
+ A : setoid, U : qpowerclass_setoid A, V : ? ⊢ (intersect_ok A) U V ≡ U ∩ V.
+ *)
nlemma test: ∀A:setoid. ∀U,V:qpowerclass A. ∀x,x':setoid1_of_setoid A. x=x' → x ∈ U ∩ V → x' ∈ U ∩ V.
#A; #U; #V; #x; #x'; #H; #p;
nqed.
(*
+alias symbol "covers" (instance 0) = "covers".
+alias symbol "covers" (instance 2) = "covers".
+alias symbol "covers" (instance 1) = "covers set".
ntheorem covers_elim2:
∀A: axiom_set. ∀U:Ω^A.∀P: A → CProp[0].
(∀a:A. a ∈ U → P a) →
##]
nqed.
+STOP
+
definition leq ≝ λA:axiom_set.λa,b:A. a ◃ {y|b=y}.
interpretation "covered by one" 'leq a b = (leq ? a b).
projects / helm.git / commitdiff
