interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun1 (concr _) __ (relS _) x y).
interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun1 ___ (relS _)).
*)
-
-include "o-basic_pairs.ma".
-(* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
-definition o_basic_pair_of_basic_pair: cic:/matita/formal_topology/basic_pairs/basic_pair.ind#xpointer(1/1) → basic_pair.
- intro;
- constructor 1;
- [ apply (SUBSETS (concr b));
- | apply (SUBSETS (form b));
- | apply (orelation_of_relation ?? (rel b)); ]
-qed.
-
-definition o_relation_pair_of_relation_pair:
- ∀BP1,BP2.cic:/matita/formal_topology/basic_pairs/relation_pair.ind#xpointer(1/1) BP1 BP2 →
- relation_pair (o_basic_pair_of_basic_pair BP1) (o_basic_pair_of_basic_pair BP2).
- intros;
- constructor 1;
- [ apply (orelation_of_relation ?? (r \sub \c));
- | apply (orelation_of_relation ?? (r \sub \f));
- | lapply (commute ?? r);
- lapply (orelation_of_relation_preserves_equality ???? Hletin);
- apply (.= (orelation_of_relation_preserves_composition (concr BP1) ??? (rel BP2)) ^ -1);
- apply (.= (orelation_of_relation_preserves_equality ???? (commute ?? r)));
- apply (orelation_of_relation_preserves_composition ?? (form BP2) (rel BP1) ?); ]
-qed.
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