-(* incluso prima non funziona piu' nulla *)
-include "o-algebra.ma".
-
-definition SUBSETS: objs1 SET → OAlgebra.
- intro A; constructor 1;
- [ apply (Ω \sup A);
- | apply subseteq;
- | apply overlaps;
- | apply big_intersects;
- | apply big_union;
- | apply ({x | True});
- simplify; intros; apply (refl1 ? (eq1 CPROP));
- | apply ({x | False});
- simplify; intros; apply (refl1 ? (eq1 CPROP));
- | intros; whd; intros; assumption
- | intros; whd; split; assumption
- | intros; apply transitive_subseteq_operator; [2: apply f; | skip | assumption]
- | intros; cases f; exists [apply w] assumption
- | intros; intros 2; apply (f ? f1 i);
- | intros; intros 2; apply f;
- (* senza questa change, universe inconsistency *)
- whd; change in ⊢ (? ? (λ_:%.?)) with (carr I);
- exists; [apply i] assumption;
- | intros 3; cases f;
- | intros 3; constructor 1;
- | intros; cases f; exists; [apply w]
- [ assumption
- | whd; intros; cases i; simplify; assumption]
- | intros; split; intro;
- [ cases f; cases x1;
- (* senza questa change, universe inconsistency *)
- change in ⊢ (? ? (λ_:%.?)) with (carr I);
- exists [apply w1] exists [apply w] assumption;
- | cases H; cases x; exists; [apply w1]
- [ assumption
- | (* senza questa change, universe inconsistency *)
- whd; change in ⊢ (? ? (λ_:%.?)) with (carr I);
- exists; [apply w] assumption]]
- | intros; intros 2; cases (f (singleton ? a) ?);
- [ exists; [apply a] [assumption | change with (a = a); apply refl1;]
- | change in x1 with (a = w); change with (mem A a q); apply (. (x1 \sup -1‡#));
- assumption]]
-qed.
+notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (⋃) \below (\emsp) term 90 p)"
+non associative with precedence 50 for @{ 'bigcup $p }.
+notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (⋃) \below (ident i ∈ I) break term 90 p)"
+non associative with precedence 50 for @{ 'bigcup_mk (λ${ident i}:$I.$p) }.
+notation > "hovbox(⋃ f)" non associative with precedence 60 for @{ 'bigcup $f }.
+
+notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (⋂) \below (\emsp) term 90 p)"
+non associative with precedence 50 for @{ 'bigcap $p }.
+notation < "hovbox(mstyle scriptlevel 1 scriptsizemultiplier 1.7 (⋂) \below (ident i ∈ I) break term 90 p)"
+non associative with precedence 50 for @{ 'bigcap_mk (λ${ident i}:$I.$p) }.
+notation > "hovbox(⋂ f)" non associative with precedence 60 for @{ 'bigcap $f }.
+
+interpretation "bigcup" 'bigcup f = (fun12 ?? (big_union ??) f).
+interpretation "bigcap" 'bigcap f = (fun12 ?? (big_intersects ??) f).
+interpretation "bigcup mk" 'bigcup_mk f = (fun12 ?? (big_union ??) (mk_unary_morphism2 ?? f ?)).
+interpretation "bigcap mk" 'bigcap_mk f = (fun12 ?? (big_intersects ??) (mk_unary_morphism2 ?? f ?)).