nrecord magma_type : Type[1] ≝
{ mtcarr:> setoid;
- op: binary_morphism mtcarr mtcarr mtcarr
+ op: unary_morphism mtcarr (unary_morph_setoid mtcarr mtcarr)
}.
nrecord magma (A: magma_type) : Type[1] ≝
- { mcarr:> qpowerclass A;
+ { mcarr:> ext_powerclass A;
op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
}.
+alias symbol "hint_decl" = "hint_decl_Type2".
unification hint 0 ≔
- A : ? ⊢ carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
+ A : ? ⊢ carr1 (ext_powerclass_setoid A) ≡ ext_powerclass A.
(*
ncoercion mcarr' : ∀A. ∀M: magma A. carr1 (qpowerclass_setoid (mtcarr A))
nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type[0] ≝
{ mmmcarr:> magma_morphism_type A B;
- mmclosed: ∀x:A. x ∈ mcarr ? Ma → mmmcarr x ∈ mcarr ? Mb
- }.
+ mmclosed: ∀x:A. x ∈ mcarr ? Ma → (fun1 ?? mmmcarr x) ∈ mcarr ? Mb
+ }. (* XXX bug nelle coercions, fun1 non inserita *)
(*
ndefinition mm_image:
ndefinition m_intersect: ∀A. magma A → magma A → magma A.
#A; #M1; #M2;
napply (mk_magma …)
- [ napply (intersect_ok ? M1 M2)
+ [ napply (intersect_is_ext_morph ? M1 M2)
| #x; #y; nwhd in ⊢ (% → % → %); *; #Hx1; #Hx2; *; #Hy1; #Hy2;
napply conj; napply op_closed; nassumption ]
nqed.
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