helm/www/lambdadelta/xslt/chc_45.xsl
helm/www/lambdadelta/xslt/xhtbl.xsl
+matita/matita/lib/lambda/.depend
+
matita/matita/contribs/lambdadelta/.depend
matita/matita/contribs/lambdadelta/bin/nodes
matita/matita/contribs/lambdadelta/bin/token
-H = @
-XOA_DIR = ../../../components/binaries/xoa
-XOA = xoa.native
-DEP_DIR = ../../../components/binaries/matitadep
-DEP = matitadep.native
-MAC_DIR = ../../../components/binaries/mac
-MAC = mac.native
+H := @
-XOA_CONF = xoa.conf.xml
-XOA_TARGETS = background/xoa_notation.ma background/xoa.ma
+TAGS := all xoa deps top
-all: xoa
- $(H)../../matitac.opt */*.ma
+all:
+ $(H)../../matitac.opt .
# xoa ########################################################################
-xoa: $(XOA_TARGETS)
+XOA_DIR := ../../../components/binaries/xoa
+XOA := xoa.native
+XOA_CONF := xoa.conf.xml
+XOA_OPTS := ../../matita.conf.xml $(XOA_CONF)
-$(XOA_TARGETS): $(XOA_CONF)
+xoa: $(XOA_CONF)
@echo " EXEC $(XOA) $(XOA_CONF)"
- $(H)MATITA_RT_BASE_DIR=../.. $(XOA_DIR)/$(XOA) $(XOA_CONF)
+ $(H)$(XOA_DIR)/$(XOA) -s $(XOA_OPTS)
+
+# dep input ##################################################################
+
+DEP_INPUT := .depend
+DEP_DIR := ../../../components/binaries/matitadep
+DEP := matitadep.native
+DEP_OPTS :=
+
+$(DEP_INPUT): MAS = $(shell find $* -name "*.ma")
+
+$(DEP_INPUT): LINE = $(MAS:%=%:include \"\".)
+
+$(DEP_INPUT): REPL = sed -e 's/^\./lambda/'
+
+$(DEP_INPUT): $(MAS) Makefile
+ @echo " GREP include"
+ $(H)grep "include \"" $(MAS) | $(REPL) > $(DEP_INPUT)
+ $(H)echo "$(LINE)" | sed -e 's/\"\. /\"\.\n/g' | $(REPL) >> $(DEP_INPUT)
# dep ########################################################################
-deps: MAS = $(shell find $* -name "*.ma")
+deps: $(DEP_INPUT)
+ @echo " MATITADEP -c"
+ $(H)$(DEP_DIR)/$(DEP) -c $(DEP_OPTS) $<
+
+# top ########################################################################
+
+top: $(DEP_INPUT)
+ @echo " MATITADEP -t"
+ $(H)$(DEP_DIR)/$(DEP) -t $(DEP_OPTS) $<
+
+##############################################################################
+
+.PHONY: $(TAGS)
-deps: $(DEP_DIR)/$(DEP)
- @echo " MATITADEP"
- $(H)grep "include \"" $(MAS) | $<
+.SUFFIXES:
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* GENERIC NOTATION *********************************************************)
-
-(* Note: this should go to core_notation *)
-notation "⊥"
- non associative with precedence 90
- for @{'false}.
-
-(* Note: this should go to core_notation *)
-notation "⊤"
- non associative with precedence 90
- for @{'true}.
-
-(* Note: this should go to core_notation *)
-notation "hvbox(a break ≺ b)"
- non associative with precedence 45
- for @{ 'prec $a $b }.
-
-notation "hvbox( # term 90 i )"
- non associative with precedence 46
- for @{ 'VariableReferenceByIndex $i }.
-
-notation "hvbox( { term 46 b } # break term 90 i )"
- non associative with precedence 46
- for @{ 'VariableReferenceByIndex $b $i }.
-
-notation "hvbox( 𝛌 . term 46 A )"
- non associative with precedence 46
- for @{ 'Abstraction $A }.
-
-notation "hvbox( { term 46 b } 𝛌 . break term 46 T)"
- non associative with precedence 46
- for @{ 'Abstraction $b $T }.
-
-notation "hvbox( 𝛌 term 46 d . break term 46 A )"
- non associative with precedence 46
- for @{ 'AnnotatedAbstraction $d $A }.
-
-notation "hvbox( @ term 46 C . break term 46 A )"
- non associative with precedence 46
- for @{ 'Application $C $A }.
-
-notation "hvbox( { term 46 b } @ break term 46 V . break term 46 T )"
- non associative with precedence 46
- for @{ 'Application $b $V $T }.
-
-notation "hvbox( ↑ [ term 46 d , break term 46 h ] break term 46 M )"
- non associative with precedence 46
- for @{ 'Lift $h $d $M }.
-
-notation > "hvbox( ↑ [ term 46 h ] break term 46 M )"
- non associative with precedence 46
- for @{ 'Lift $h 0 $M }.
-
-notation > "hvbox( ↑ term 46 M )"
- non associative with precedence 46
- for @{ 'Lift 1 0 $M }.
-
-(* Note: the notation with "/" does not work *)
-notation "hvbox( [ term 46 d break ↙ term 46 N ] break term 46 M )"
- non associative with precedence 46
- for @{ 'DSubst $N $d $M }.
-
-notation > "hvbox( [ ↙ term 46 N ] break term 46 M )"
- non associative with precedence 46
- for @{ 'DSubst $N 0 $M }.
-
-(* Note: we do not use → since it is reserved by CIC *)
-notation "hvbox( M break ↦ term 46 N )"
- non associative with precedence 45
- for @{ 'SeqRed $M $N }.
-
-notation "hvbox( M break ↦ [ term 46 p ] break term 46 N )"
- non associative with precedence 45
- for @{ 'SeqRed $M $p $N }.
-
-notation "hvbox( M break ↦* term 46 N )"
- non associative with precedence 45
- for @{ 'SeqRedStar $M $N }.
-
-notation "hvbox( M break ↦* [ term 46 s ] break term 46 N )"
- non associative with precedence 45
- for @{ 'SeqRedStar $M $s $N }.
-
-notation "hvbox( M break ⤇ term 46 N )"
- non associative with precedence 45
- for @{ 'ParRed $M $N }.
-
-notation "hvbox( M break ⤇* term 46 N )"
- non associative with precedence 45
- for @{ 'ParRedStar $M $N }.
include "basics/lists/lstar.ma".
include "arithmetics/exp.ma".
-include "lambda/background/xoa_notation.ma".
-include "lambda/background/xoa.ma".
-include "lambda/background/notation.ma".
+include "lambda/notation/xoa/false_0.ma".
+include "lambda/notation/xoa/true_0.ma".
+include "lambda/xoa/or_3.ma".
+include "lambda/xoa/ex_1_2.ma".
+include "lambda/xoa/ex_3_2.ma".
+include "lambda/xoa/ex_3_3.ma".
+
+include "lambda/notation/functions/nil_0.ma".
+include "lambda/notation/functions/hocons_2.ma".
(* logic *)
(* lists *)
-(* Note: notation for nil not involving brackets *)
-notation > "◊"
- non associative with precedence 90
- for @{'nil}.
-
lemma list_inv: ∀A. ∀l:list A. ◊ = l ∨ ∃∃a0,l0. a0 :: l0 = l.
#A * /2 width=1/ /3 width=3/
qed-.
interpretation "map_cons" 'ho_cons a l = (map_cons ? a l).
-notation "hvbox(a ::: break l)"
- right associative with precedence 47
- for @{'ho_cons $a $l}.
-
lemma map_cons_inv_nil: ∀A,a,l1. map_cons A a l1 = ◊ → ◊ = l1.
#A #a * // normalize #a1 #l1 #H destruct
qed-.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* This file was generated by xoa.native: do not edit *********************)
-
-include "basics/pts.ma".
-
-include "lambda/background/xoa_notation.ma".
-
-(* multiple existental quantifier (1, 2) *)
-
-inductive ex1_2 (A0,A1:Type[0]) (P0:A0→A1→Prop) : Prop ≝
- | ex1_2_intro: ∀x0,x1. P0 x0 x1 → ex1_2 ? ? ?
-.
-
-interpretation "multiple existental quantifier (1, 2)" 'Ex P0 = (ex1_2 ? ? P0).
-
-(* multiple existental quantifier (2, 2) *)
-
-inductive ex2_2 (A0,A1:Type[0]) (P0,P1:A0→A1→Prop) : Prop ≝
- | ex2_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → ex2_2 ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (2, 2)" 'Ex P0 P1 = (ex2_2 ? ? P0 P1).
-
-(* multiple existental quantifier (2, 3) *)
-
-inductive ex2_3 (A0,A1,A2:Type[0]) (P0,P1:A0→A1→A2→Prop) : Prop ≝
- | ex2_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → ex2_3 ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (2, 3)" 'Ex P0 P1 = (ex2_3 ? ? ? P0 P1).
-
-(* multiple existental quantifier (3, 1) *)
-
-inductive ex3 (A0:Type[0]) (P0,P1,P2:A0→Prop) : Prop ≝
- | ex3_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → ex3 ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (3, 1)" 'Ex P0 P1 P2 = (ex3 ? P0 P1 P2).
-
-(* multiple existental quantifier (3, 2) *)
-
-inductive ex3_2 (A0,A1:Type[0]) (P0,P1,P2:A0→A1→Prop) : Prop ≝
- | ex3_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → ex3_2 ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (3, 2)" 'Ex P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
-
-(* multiple existental quantifier (3, 3) *)
-
-inductive ex3_3 (A0,A1,A2:Type[0]) (P0,P1,P2:A0→A1→A2→Prop) : Prop ≝
- | ex3_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → ex3_3 ? ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (3, 3)" 'Ex P0 P1 P2 = (ex3_3 ? ? ? P0 P1 P2).
-
-(* multiple existental quantifier (3, 4) *)
-
-inductive ex3_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2:A0→A1→A2→A3→Prop) : Prop ≝
- | ex3_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → ex3_4 ? ? ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (3, 4)" 'Ex P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
-
-(* multiple existental quantifier (4, 1) *)
-
-inductive ex4 (A0:Type[0]) (P0,P1,P2,P3:A0→Prop) : Prop ≝
- | ex4_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → P3 x0 → ex4 ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (4, 1)" 'Ex P0 P1 P2 P3 = (ex4 ? P0 P1 P2 P3).
-
-(* multiple existental quantifier (4, 2) *)
-
-inductive ex4_2 (A0,A1:Type[0]) (P0,P1,P2,P3:A0→A1→Prop) : Prop ≝
- | ex4_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → P3 x0 x1 → ex4_2 ? ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (4, 2)" 'Ex P0 P1 P2 P3 = (ex4_2 ? ? P0 P1 P2 P3).
-
-(* multiple existental quantifier (4, 3) *)
-
-inductive ex4_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3:A0→A1→A2→Prop) : Prop ≝
- | ex4_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → ex4_3 ? ? ? ? ? ? ?
-.
-
-interpretation "multiple existental quantifier (4, 3)" 'Ex P0 P1 P2 P3 = (ex4_3 ? ? ? P0 P1 P2 P3).
-
-(* multiple disjunction connective (3) *)
-
-inductive or3 (P0,P1,P2:Prop) : Prop ≝
- | or3_intro0: P0 → or3 ? ? ?
- | or3_intro1: P1 → or3 ? ? ?
- | or3_intro2: P2 → or3 ? ? ?
-.
-
-interpretation "multiple disjunction connective (3)" 'Or P0 P1 P2 = (or3 P0 P1 P2).
-
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* This file was generated by xoa.native: do not edit *********************)
-
-(* multiple existental quantifier (1, 2) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.$P0) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) }.
-
-(* multiple existental quantifier (2, 2) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) }.
-
-(* multiple existental quantifier (2, 3) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) }.
-
-(* multiple existental quantifier (3, 1) *)
-
-notation > "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.$P0) (λ${ident x0}.$P1) (λ${ident x0}.$P2) }.
-
-notation < "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.$P0) (λ${ident x0}:$T0.$P1) (λ${ident x0}:$T0.$P2) }.
-
-(* multiple existental quantifier (3, 2) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) (λ${ident x0}.λ${ident x1}.$P2) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P2) }.
-
-(* multiple existental quantifier (3, 3) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P2) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P2) }.
-
-(* multiple existental quantifier (3, 4) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 , ident x3 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P2) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 , ident x3 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P2) }.
-
-(* multiple existental quantifier (4, 1) *)
-
-notation > "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.$P0) (λ${ident x0}.$P1) (λ${ident x0}.$P2) (λ${ident x0}.$P3) }.
-
-notation < "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.$P0) (λ${ident x0}:$T0.$P1) (λ${ident x0}:$T0.$P2) (λ${ident x0}:$T0.$P3) }.
-
-(* multiple existental quantifier (4, 2) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) (λ${ident x0}.λ${ident x1}.$P2) (λ${ident x0}.λ${ident x1}.$P3) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P2) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P3) }.
-
-(* multiple existental quantifier (4, 3) *)
-
-notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P2) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P3) }.
-
-notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
- non associative with precedence 20
- for @{ 'Ex (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P2) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P3) }.
-
-(* multiple disjunction connective (3) *)
-
-notation "hvbox(∨∨ term 29 P0 break | term 29 P1 break | term 29 P2)"
- non associative with precedence 30
- for @{ 'Or $P0 $P1 $P2 }.
-
include "lambda/levels/term.ma".
+include "lambda/notation/functions/annotatedabstraction_2.ma".
+
(* ITERATED ABSTRACTION *****************************************************)
definition labst: nat → lterm → lterm ≝ λh,M. match M with
include "lambda/background/preamble.ma".
+include "lambda/notation/functions/variablereferencebylevel_2.ma".
+include "lambda/notation/functions/application_3.ma".
+
(* PER LEVEL TERM STRUCTURE *************************************************)
(* Policy: term metavariables : A, B, C, D, M, N
interpretation "stratified term construction (application)"
'Application i C A = (LAppl i C A).
-
-notation "hvbox( { term 46 b } § break term 90 d )"
- non associative with precedence 46
- for @{ 'VariableReferenceByLevel $b $d }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( 𝛌 . term 46 A )"
+ non associative with precedence 46
+ for @{ 'Abstraction $A }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } 𝛌 . break term 46 T)"
+ non associative with precedence 46
+ for @{ 'Abstraction $b $T }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( 𝛌 term 46 d . break term 46 A )"
+ non associative with precedence 46
+ for @{ 'AnnotatedAbstraction $d $A }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( @ term 46 C . break term 46 A )"
+ non associative with precedence 46
+ for @{ 'Application $C $A }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } @ break term 46 V . break term 46 T )"
+ non associative with precedence 46
+ for @{ 'Application $b $V $T }.
(**************************************************************************)
notation "hvbox( ⇓ term 46 M )"
- non associative with precedence 46
- for @{ 'Backward $M }.
+ non associative with precedence 46
+ for @{ 'Backward $M }.
(**************************************************************************)
notation "hvbox( ⇓ [ term 46 d , break term 46 h ] break term 46 M )"
- non associative with precedence 46
- for @{ 'Backward $h $d $M }.
+ non associative with precedence 46
+ for @{ 'Backward $h $d $M }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: the notation with "/" does not work *)
+notation "hvbox( [ term 46 d break ↙ term 46 N ] break term 46 M )"
+ non associative with precedence 46
+ for @{ 'DSubst $N $d $M }.
+
+notation > "hvbox( [ ↙ term 46 N ] break term 46 M )"
+ non associative with precedence 46
+ for @{ 'DSubst $N 0 $M }.
(**************************************************************************)
notation "hvbox( ⇑ term 46 M )"
- non associative with precedence 46
- for @{ 'Forward $M }.
+ non associative with precedence 46
+ for @{ 'Forward $M }.
(**************************************************************************)
notation "hvbox( ⇑ [ term 46 d, break term 46 h ] break term 46 M )"
- non associative with precedence 46
- for @{ 'Forward $h $d $M }.
+ non associative with precedence 46
+ for @{ 'Forward $h $d $M }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox(a ::: break l)"
+ right associative with precedence 47
+ for @{'ho_cons $a $l}.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( ↑ [ term 46 d , break term 46 h ] break term 46 M )"
+ non associative with precedence 46
+ for @{ 'Lift $h $d $M }.
+
+notation > "hvbox( ↑ [ term 46 h ] break term 46 M )"
+ non associative with precedence 46
+ for @{ 'Lift $h 0 $M }.
+
+notation > "hvbox( ↑ term 46 M )"
+ non associative with precedence 46
+ for @{ 'Lift 1 0 $M }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( ♯{ term 46 M } )"
+ non associative with precedence 90
+ for @{ 'Multiplicity $M }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: notation for nil not involving brackets *)
+notation > "◊"
+ non associative with precedence 90
+ for @{'nil}.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox(⇓ term 46 F)"
+ non associative with precedence 46
+ for @{ 'ProjectDown $F }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } ⇕ break term 46 F)"
+ non associative with precedence 46
+ for @{ 'ProjectSame $b $F }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } ⇑ break term 46 M)"
+ non associative with precedence 46
+ for @{ 'ProjectUp $b $M }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( # term 90 i )"
+ non associative with precedence 46
+ for @{ 'VariableReferenceByIndex $i }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } # break term 90 i )"
+ non associative with precedence 46
+ for @{ 'VariableReferenceByIndex $b $i }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( { term 46 b } § break term 90 d )"
+ non associative with precedence 46
+ for @{ 'VariableReferenceByLevel $b $d }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ⓢ↦* term 46 N )"
+ non associative with precedence 45
+ for @{ 'DecomposedStd $M $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ⤇ term 46 N )"
+ non associative with precedence 45
+ for @{ 'ParRed $M $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ⤇* term 46 N )"
+ non associative with precedence 45
+ for @{ 'ParRedStar $M $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: this should go to core_notation *)
+notation "hvbox(a break ≺ b)"
+ non associative with precedence 45
+ for @{ 'prec $a $b }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: we do not use → since it is reserved by CIC *)
+notation "hvbox( M break ↦ term 46 N )"
+ non associative with precedence 45
+ for @{ 'SeqRed $M $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ↦ [ term 46 p ] break term 46 N )"
+ non associative with precedence 45
+ for @{ 'SeqRed $M $p $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ↦* term 46 N )"
+ non associative with precedence 45
+ for @{ 'SeqRedStar $M $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( M break ↦* [ term 46 s ] break term 46 N )"
+ non associative with precedence 45
+ for @{ 'SeqRedStar $M $s $N }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( F break Ⓡ ↦ [ term 46 p ] break term 46 G )"
+ non associative with precedence 45
+ for @{ 'Std $F $p $G }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+notation "hvbox( F break Ⓡ ↦* [ term 46 p ] break term 46 G )"
+ non associative with precedence 45
+ for @{ 'StdStar $F $p $G }.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (1, 2) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}.λ${ident x1}.$P0) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (2, 2) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (2, 3) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (3, 1) *)
+
+notation > "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0}.$P0) (λ${ident x0}.$P1) (λ${ident x0}.$P2) }.
+
+notation < "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0}:$T0.$P0) (λ${ident x0}:$T0.$P1) (λ${ident x0}:$T0.$P2) }.
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (3, 2) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) (λ${ident x0}.λ${ident x1}.$P2) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P2) }.
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (3, 3) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P2) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P2) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (3, 4) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 , ident x3 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex4 (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.λ${ident x3}.$P2) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 , ident x3 break . term 19 P0 break & term 19 P1 break & term 19 P2)"
+ non associative with precedence 20
+ for @{ 'Ex4 (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.λ${ident x3}:$T3.$P2) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (4, 1) *)
+
+notation > "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0}.$P0) (λ${ident x0}.$P1) (λ${ident x0}.$P2) (λ${ident x0}.$P3) }.
+
+notation < "hvbox(∃∃ ident x0 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex (λ${ident x0}:$T0.$P0) (λ${ident x0}:$T0.$P1) (λ${ident x0}:$T0.$P2) (λ${ident x0}:$T0.$P3) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (4, 2) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}.λ${ident x1}.$P0) (λ${ident x0}.λ${ident x1}.$P1) (λ${ident x0}.λ${ident x1}.$P2) (λ${ident x0}.λ${ident x1}.$P3) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex2 (λ${ident x0}:$T0.λ${ident x1}:$T1.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P2) (λ${ident x0}:$T0.λ${ident x1}:$T1.$P3) }.
+
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple existental quantifier (4, 3) *)
+
+notation > "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P0) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P1) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P2) (λ${ident x0}.λ${ident x1}.λ${ident x2}.$P3) }.
+
+notation < "hvbox(∃∃ ident x0 , ident x1 , ident x2 break . term 19 P0 break & term 19 P1 break & term 19 P2 break & term 19 P3)"
+ non associative with precedence 20
+ for @{ 'Ex3 (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P0) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P1) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P2) (λ${ident x0}:$T0.λ${ident x1}:$T1.λ${ident x2}:$T2.$P3) }.
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: this should go to core_notation *)
+notation "⊥"
+ non associative with precedence 90
+ for @{'false}.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+(* multiple disjunction connective (3) *)
+
+notation "hvbox(∨∨ term 29 P0 break | term 29 P1 break | term 29 P2)"
+ non associative with precedence 30
+ for @{ 'Or $P0 $P1 $P2 }.
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* Note: this should go to core_notation *)
+notation "⊤"
+ non associative with precedence 90
+ for @{'true}.
include "lambda/paths/standard_trace.ma".
include "lambda/paths/labeled_sequential_computation.ma".
+include "lambda/notation/relations/decomposedstd_2.ma".
+
(* DECOMPOSED STANDARD COMPUTATION ***********************************************)
(* Note: this is the "standard" computation of:
interpretation "decomposed standard computation"
'DecomposedStd M N = (dst M N).
-notation "hvbox( M break ⓢ↦* term 46 N )"
- non associative with precedence 45
- for @{ 'DecomposedStd $M $N }.
-
lemma dst_inv_lref: ∀M,N. M ⓢ↦* N → ∀j. #j = N →
∃∃s. is_whd s & M ↦*[s] #j.
#M #N * -M -N
include "lambda/paths/trace.ma".
include "lambda/paths/labeled_sequential_reduction.ma".
+include "lambda/notation/relations/seqredstar_3.ma".
+
(* PATH-LABELED SEQUENTIAL COMPUTATION (MULTISTEP) *******************************)
(* Note: lstar shuld be replaced by l_sreds *)
include "lambda/paths/path.ma".
include "lambda/terms/sequential_reduction.ma".
+include "lambda/notation/relations/seqred_3.ma".
+
+include "lambda/xoa/ex_2_2.ma".
+
(* PATH-LABELED SEQUENTIAL REDUCTION (SINGLE STEP) **************************)
inductive pl_sred: path → relation term ≝
include "lambda/paths/labeled_sequential_computation.ma".
include "lambda/paths/labeled_st_reduction.ma".
+include "lambda/notation/relations/stdstar_3.ma".
+
+include "lambda/xoa/ex_2_3.ma".
+
(* PATH-LABELED STANDARD COMPUTATION (MULTISTEP) ****************************)
(* Note: lstar shuld be replaced by l_sreds *)
interpretation "path-labeled standard reduction"
'StdStar F p G = (pl_sts p F G).
-notation "hvbox( F break Ⓡ ↦* [ term 46 p ] break term 46 G )"
- non associative with precedence 45
- for @{ 'StdStar $F $p $G }.
-
lemma pl_sts_fwd_pl_sreds: ∀s,F1,F2. F1 Ⓡ↦*[s] F2 → ⇓F1 ↦*[s] ⇓F2.
#s #F1 #F2 #H @(lstar_ind_r … s F2 H) -s -F2 //
#p #s #F #F2 #_ #HF2 #IHF1
include "lambda/paths/labeled_sequential_reduction.ma".
include "lambda/paths/standard_order.ma".
+include "lambda/notation/relations/std_3.ma".
+
+include "lambda/xoa/ex_4_1.ma".
+include "lambda/xoa/ex_3_4.ma".
+
(* PATH-LABELED STANDARD REDUCTION ON SUBTERMS (SINGLE STEP) ****************)
(* Note: this is standard reduction on marked redexes,
interpretation "path-labeled standard reduction"
'Std F p G = (pl_st p F G).
-notation "hvbox( F break Ⓡ ↦ [ term 46 p ] break term 46 G )"
- non associative with precedence 45
- for @{ 'Std $F $p $G }.
-
lemma pl_st_fwd_pl_sred: ∀p,F1,F2. F1 Ⓡ↦[p] F2 → ⇓F1 ↦[p] ⇓F2.
#p #F1 #F2 #H elim H -p -F1 -F2 normalize /2 width=1/
qed-.
include "lambda/paths/path.ma".
+include "lambda/notation/relations/prec_2.ma".
+
(* STANDARD PRECEDENCE ******************************************************)
(* Note: standard precedence relation on paths: p ≺ q
include "lambda/subterms/carrier.ma".
+include "lambda/notation/functions/projectup_2.ma".
+
+include "lambda/xoa/ex_3_1.ma".
+include "lambda/xoa/ex_4_2.ma".
+
(* BOOLEAN (EMPTY OR FULL) SUBSET *******************************************)
let rec boolean b M on M ≝ match M with
interpretation "boolean subset (subterms)"
'ProjectUp b M = (boolean b M).
-notation "hvbox( { term 46 b } ⇑ break term 46 M)"
- non associative with precedence 46
- for @{ 'ProjectUp $b $M }.
-
lemma boolean_inv_vref: ∀j,c,b,M. {b}⇑ M = {c}#j → b = c ∧ M = #j.
#j #c #b * normalize
[ #i #H destruct /2 width=1/
include "lambda/subterms/boolean.ma".
+include "lambda/notation/functions/projectsame_2.ma".
+
+include "lambda/xoa/ex_4_3.ma".
+
(* BOOLEANIZED SUBSET (EMPTY OR FULL) ***************************************)
definition booleanized: bool → subterms → subterms ≝
interpretation "booleanized (subterms)"
'ProjectSame b F = (booleanized b F).
-notation "hvbox( { term 46 b } ⇕ break term 46 F)"
- non associative with precedence 46
- for @{ 'ProjectSame $b $F }.
-
lemma booleanized_inv_vref: ∀j,c,b,F. {b}⇕ F = {c}#j →
∃∃b1. b = c & F = {b1}#j.
#j #c #b #F #H
include "lambda/terms/relocating_substitution.ma".
include "lambda/subterms/relocating_substitution.ma".
+include "lambda/notation/functions/projectdown_1.ma".
+
+include "lambda/xoa/ex_2_2.ma".
+
(* CARRIER (UNDERLYING TERM) ************************************************)
let rec carrier F on F ≝ match F with
interpretation "carrier (subterms)"
'ProjectDown F = (carrier F).
-notation "hvbox(⇓ term 46 F)"
- non associative with precedence 46
- for @{ 'ProjectDown $F }.
-
lemma carrier_inv_vref: ∀j,F. ⇓F = #j → ∃b. F = {b}#j.
#j * normalize
[ #b #i #H destruct /2 width=2/
include "lambda/subterms/relocation.ma".
+include "lambda/notation/functions/dsubst_3.ma".
+
(* RELOCATING SUBSTITUTION **************************************************)
(* Policy: depth (level) metavariables: d, e (as for lift) *)
include "lambda/subterms/subterms.ma".
+include "lambda/notation/functions/lift_3.ma".
+
(* RELOCATION FOR SUBTERMS **************************************************)
let rec slift h d E on E ≝ match E with
include "lambda/background/preamble.ma".
+include "lambda/notation/functions/variablereferencebyindex_2.ma".
+include "lambda/notation/functions/abstraction_2.ma".
+include "lambda/notation/functions/application_3.ma".
+
(* SUBSETS OF SUBTERMS ******************************************************)
(* Policy: boolean marks metavariables: b,c
include "lambda/terms/term.ma".
+include "lambda/notation/functions/annotatedabstraction_2.ma".
+
(* ITERATED ABSTRACTION *****************************************************)
let rec abst d M on d ≝ match d with
include "lambda/terms/relocating_substitution.ma".
+include "lambda/notation/functions/multiplicity_1.ma".
+
(* MULTIPLICITY *************************************************************)
(* Note: this gives the number of variable references in M *)
interpretation "term multiplicity"
'Multiplicity M = (mult M).
-notation "hvbox( ♯{ term 46 M } )"
- non associative with precedence 90
- for @{ 'Multiplicity $M }.
-
lemma mult_positive: ∀M. 0 < ♯{M}.
#M elim M -M // /2 width=1/
qed.
include "lambda/terms/parallel_reduction.ma".
+include "lambda/notation/relations/parredstar_2.ma".
+
(* PARALLEL COMPUTATION (MULTISTEP) *****************************************)
definition preds: relation term ≝ star … pred.
include "lambda/terms/size.ma".
include "lambda/terms/sequential_reduction.ma".
+include "lambda/notation/relations/parred_2.ma".
+
+include "lambda/xoa/ex_4_3.ma".
+
(* PARALLEL REDUCTION (SINGLE STEP) *****************************************)
(* Note: the application "(A B)" is represented by "@B.A"
include "lambda/terms/relocation.ma".
+include "lambda/notation/functions/dsubst_3.ma".
+
(* RELOCATING SUBSTITUTION **************************************************)
(* Policy: depth (level) metavariables: d, e (as for lift) *)
include "lambda/terms/term.ma".
+include "lambda/notation/functions/lift_3.ma".
+
(* RELOCATION ***************************************************************)
(* Policy: level metavariables : d, e
include "lambda/terms/parallel_computation.ma".
+include "lambda/notation/relations/seqredstar_2.ma".
+
(* SEQUENTIAL COMPUTATION (MULTISTEP) ***************************************)
definition sreds: relation term ≝ star … sred.
include "lambda/terms/multiplicity.ma".
+include "lambda/notation/relations/seqred_2.ma".
+
(* SEQUENTIAL REDUCTION (SINGLE STEP) ***************************************)
(* Note: the application "(A B)" is represented by "@B.A" following:
include "lambda/background/preamble.ma".
+include "lambda/notation/functions/variablereferencebyindex_1.ma".
+include "lambda/notation/functions/abstraction_1.ma".
+include "lambda/notation/functions/application_2.ma".
+
(* TERM STRUCTURE ***********************************************************)
(* Policy: term metavariables : A, B, C, D, M, N
<?xml version="1.0" encoding="utf-8"?>
<helm_registry>
- <section name="matita">
- <key name="rt_base_dir">$(MATITA_RT_BASE_DIR)</key>
- </section>
<section name="xoa">
- <key name="output_dir">lib/</key>
- <key name="objects">lambda/background/xoa</key>
- <key name="notations">lambda/background/xoa_notation</key>
+ <key name="output_dir">..</key>
+ <key name="objects">lambda/xoa</key>
+ <key name="notations">lambda/notation/xoa</key>
<key name="include">basics/pts.ma</key>
<key name="ex">1 2</key>
<key name="ex">2 2</key>
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_1_2.ma".
+
+(* multiple existental quantifier (1, 2) *)
+
+inductive ex1_2 (A0,A1:Type[0]) (P0:A0→A1→Prop) : Prop ≝
+ | ex1_2_intro: ∀x0,x1. P0 x0 x1 → ex1_2 ? ? ?
+.
+
+interpretation "multiple existental quantifier (1, 2)" 'Ex2 P0 = (ex1_2 ? ? P0).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_2_2.ma".
+
+(* multiple existental quantifier (2, 2) *)
+
+inductive ex2_2 (A0,A1:Type[0]) (P0,P1:A0→A1→Prop) : Prop ≝
+ | ex2_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → ex2_2 ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (2, 2)" 'Ex2 P0 P1 = (ex2_2 ? ? P0 P1).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_2_3.ma".
+
+(* multiple existental quantifier (2, 3) *)
+
+inductive ex2_3 (A0,A1,A2:Type[0]) (P0,P1:A0→A1→A2→Prop) : Prop ≝
+ | ex2_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → ex2_3 ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (2, 3)" 'Ex3 P0 P1 = (ex2_3 ? ? ? P0 P1).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_3_1.ma".
+
+(* multiple existental quantifier (3, 1) *)
+
+inductive ex3 (A0:Type[0]) (P0,P1,P2:A0→Prop) : Prop ≝
+ | ex3_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → ex3 ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (3, 1)" 'Ex P0 P1 P2 = (ex3 ? P0 P1 P2).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_3_2.ma".
+
+(* multiple existental quantifier (3, 2) *)
+
+inductive ex3_2 (A0,A1:Type[0]) (P0,P1,P2:A0→A1→Prop) : Prop ≝
+ | ex3_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → ex3_2 ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (3, 2)" 'Ex2 P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_3_3.ma".
+
+(* multiple existental quantifier (3, 3) *)
+
+inductive ex3_3 (A0,A1,A2:Type[0]) (P0,P1,P2:A0→A1→A2→Prop) : Prop ≝
+ | ex3_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → ex3_3 ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (3, 3)" 'Ex3 P0 P1 P2 = (ex3_3 ? ? ? P0 P1 P2).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_3_4.ma".
+
+(* multiple existental quantifier (3, 4) *)
+
+inductive ex3_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2:A0→A1→A2→A3→Prop) : Prop ≝
+ | ex3_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → ex3_4 ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (3, 4)" 'Ex4 P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_4_1.ma".
+
+(* multiple existental quantifier (4, 1) *)
+
+inductive ex4 (A0:Type[0]) (P0,P1,P2,P3:A0→Prop) : Prop ≝
+ | ex4_intro: ∀x0. P0 x0 → P1 x0 → P2 x0 → P3 x0 → ex4 ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (4, 1)" 'Ex P0 P1 P2 P3 = (ex4 ? P0 P1 P2 P3).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_4_2.ma".
+
+(* multiple existental quantifier (4, 2) *)
+
+inductive ex4_2 (A0,A1:Type[0]) (P0,P1,P2,P3:A0→A1→Prop) : Prop ≝
+ | ex4_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → P3 x0 x1 → ex4_2 ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (4, 2)" 'Ex2 P0 P1 P2 P3 = (ex4_2 ? ? P0 P1 P2 P3).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/ex_4_3.ma".
+
+(* multiple existental quantifier (4, 3) *)
+
+inductive ex4_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3:A0→A1→A2→Prop) : Prop ≝
+ | ex4_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → ex4_3 ? ? ? ? ? ? ?
+.
+
+interpretation "multiple existental quantifier (4, 3)" 'Ex3 P0 P1 P2 P3 = (ex4_3 ? ? ? P0 P1 P2 P3).
+
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* This file was generated by xoa.native: do not edit *********************)
+
+include "basics/pts.ma".
+
+include "lambda/notation/xoa/or_3.ma".
+
+(* multiple disjunction connective (3) *)
+
+inductive or3 (P0,P1,P2:Prop) : Prop ≝
+ | or3_intro0: P0 → or3 ? ? ?
+ | or3_intro1: P1 → or3 ? ? ?
+ | or3_intro2: P2 → or3 ? ? ?
+.
+
+interpretation "multiple disjunction connective (3)" 'Or P0 P1 P2 = (or3 P0 P1 P2).
+
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