- intros 5;
- whd in e; unfold BTop_to_OBTop in e; simplify in e;
- change in match (oA ?) in e with (A o1);
- whd in f g;
- alias symbol "OR_f_minus_star" (instance 1) = "relation f⎻*".
- change in match ((o_continuous_relation_of_continuous_relation_morphism o1 o2 f)⎻* ) in e with ((foo ?? f)⎻* );
- change in match ((o_continuous_relation_of_continuous_relation_morphism o1 o2 g)⎻* ) in e with ((foo ?? g)⎻* );
- whd; whd in o1 o2;
- intro b;
- alias symbol "OR_f_minus" (instance 1) = "relation f⎻".
- letin fb ≝ ((ext ?? f) b);
- lapply (e fb);
- whd in Hletin:(? ? ? % %);
- cases (Hletin); simplify in s s1;
- split;
- [2: intro; simplify;
- lapply depth=0 (s b); intro; apply (Hletin1 ? a ?)
- [ 2: whd in f1;
- change in Hletin with ((foo ?? f)⎻*
-
- alias symbol "OR_f_minus_star" (instance 4) = "relation f⎻*".
- alias symbol "OR_f_minus_star" (instance 4) = "relation f⎻*".
-change in e with
- (comp2 SET1 (Ω^o1) (Ω^o1) (Ω^o2) (A o1) (foo o1 o2 f)⎻* =_1
- comp2 SET1 (Ω^o1) (Ω^o1) (Ω^o2) (A o1) (foo o1 o2 g)⎻*
- );
-
-
-
- change in e with (comp1 SET (Ω^o1) ?? (A o1) (foo o1 o2 f)⎻* = ((foo o1 o2 g)⎻* ∘ A o1));
- unfold o_continuous_relation_of_continuous_relation_morphism in e;
- unfold o_continuous_relation_of_continuous_relation in e;
- simplify in e;