qed.
interpretation "unary morphism comprehension with no proof" 'comprehension T P =
- (mk_unary_morphism T _ P _).
+ (mk_unary_morphism T ? P ?).
interpretation "unary morphism1 comprehension with no proof" 'comprehension T P =
- (mk_unary_morphism1 T _ P _).
+ (mk_unary_morphism1 T ? P ?).
notation > "hvbox({ ident i ∈ s | term 19 p | by })" with precedence 90
for @{ 'comprehension_by $s (λ${ident i}. $p) $by}.
for @{ 'comprehension_by $s (λ${ident i}:$_. $p) $by}.
interpretation "unary morphism comprehension with proof" 'comprehension_by s \eta.f p =
- (mk_unary_morphism s _ f p).
+ (mk_unary_morphism s ? f p).
interpretation "unary morphism1 comprehension with proof" 'comprehension_by s \eta.f p =
- (mk_unary_morphism1 s _ f p).
+ (mk_unary_morphism1 s ? f p).
(* per il set-indexing vedere capitolo BPTools (foundational tools), Sect. 0.3.4 complete
lattices, Definizione 0.9 *)
∀p,q.(∀r.oa_overlap p r → oa_overlap q r) → oa_leq p q
}.
-interpretation "o-algebra leq" 'leq a b = (fun21 ___ (oa_leq _) a b).
+interpretation "o-algebra leq" 'leq a b = (fun21 ??? (oa_leq ?) a b).
notation "hovbox(a mpadded width -150% (>)< b)" non associative with precedence 45
for @{ 'overlap $a $b}.
-interpretation "o-algebra overlap" 'overlap a b = (fun21 ___ (oa_overlap _) a b).
+interpretation "o-algebra overlap" 'overlap a b = (fun21 ??? (oa_overlap ?) a b).
notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (∧) \below (\emsp) \nbsp term 90 p)"
non associative with precedence 50 for @{ 'oa_meet $p }.
notation > "hovbox(∧ f)" non associative with precedence 60
for @{ 'oa_meet $f }.
interpretation "o-algebra meet" 'oa_meet f =
- (fun12 __ (oa_meet __) f).
+ (fun12 ?? (oa_meet ??) f).
interpretation "o-algebra meet with explicit function" 'oa_meet_mk f =
- (fun12 __ (oa_meet __) (mk_unary_morphism _ _ f _)).
+ (fun12 ?? (oa_meet ??) (mk_unary_morphism ?? f ?)).
notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (∨) \below (\emsp) \nbsp term 90 p)"
non associative with precedence 50 for @{ 'oa_join $p }.
notation > "hovbox(∨ f)" non associative with precedence 60
for @{ 'oa_join $f }.
interpretation "o-algebra join" 'oa_join f =
- (fun12 __ (oa_join __) f).
+ (fun12 ?? (oa_join ??) f).
interpretation "o-algebra join with explicit function" 'oa_join_mk f =
- (fun12 __ (oa_join __) (mk_unary_morphism _ _ f _)).
+ (fun12 ?? (oa_join ??) (mk_unary_morphism ?? f ?)).
definition binary_meet : ∀O:OAlgebra. binary_morphism1 O O O.
intros; split;
qed.
interpretation "o-algebra binary meet" 'and a b =
- (fun21 ___ (binary_meet _) a b).
+ (fun21 ??? (binary_meet ?) a b).
prefer coercion Type1_OF_OAlgebra.
qed.
interpretation "o-algebra binary join" 'or a b =
- (fun21 ___ (binary_join _) a b).
+ (fun21 ??? (binary_join ?) a b).
lemma oa_overlap_preservers_meet: ∀O:OAlgebra.∀p,q:O.p >< q → p >< (p ∧ q).
(* next change to avoid universe inconsistency *)
for @{ 'oa_join (mk_unary_morphism BOOL ? (λx__:bool.match x__ with [ true ⇒ $a | false ⇒ $b ]) (IF_THEN_ELSE_p ? $a $b)) }.
interpretation "o-algebra join" 'oa_join f =
- (fun12 __ (oa_join __) f).
+ (fun12 ?? (oa_join ??) f).
interpretation "o-algebra join with explicit function" 'oa_join_mk f =
- (fun12 __ (oa_join __) (mk_unary_morphism _ _ f _)).
+ (fun12 ?? (oa_join ??) (mk_unary_morphism ?? f ?)).
record ORelation (P,Q : OAlgebra) : Type2 ≝ {
or_f_ : carr2 (P ⇒ Q);
notation "r \sup ⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
notation > "r⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
-interpretation "o-relation f⎻*" 'OR_f_minus_star r = (fun12 __ (or_f_minus_star _ _) r).
-interpretation "o-relation f⎻" 'OR_f_minus r = (fun12 __ (or_f_minus _ _) r).
-interpretation "o-relation f*" 'OR_f_star r = (fun12 __ (or_f_star _ _) r).
+interpretation "o-relation f⎻*" 'OR_f_minus_star r = (fun12 ?? (or_f_minus_star ? ?) r).
+interpretation "o-relation f⎻" 'OR_f_minus r = (fun12 ?? (or_f_minus ? ?) r).
+interpretation "o-relation f*" 'OR_f_star r = (fun12 ?? (or_f_star ? ?) r).
definition or_prop1 : ∀P,Q:OAlgebra.∀F:ORelation_setoid P Q.∀p,q.
(F p ≤ q) = (p ≤ F* q).