include "datatypes/pairs.ma".
alias symbol "eq" = "setoid eq".
-
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
nrecord partition (A: setoid) : Type[1] ≝
{ support: setoid;
- indexes: qpowerclass support;
- class: unary_morphism1 (setoid1_of_setoid support) (qpowerclass_setoid A);
+ indexes: ext_powerclass support;
+ class: unary_morphism1 (setoid1_of_setoid support) (ext_powerclass_setoid A);
inhabited: ∀i. i ∈ indexes → class i ≬ class i;
disjoint: ∀i,j. i ∈ indexes → j ∈ indexes → class i ≬ class j → i = j;
covers: big_union support ? indexes (λx.class x) = full_set A
nlapply(disjoint … P (f i1) (f i1') ???)
[##2,3: napply f_closed; nassumption
|##1: @ (fi i1 i2); @;
- ##[ napply f_closed; nassumption ##| napply (. E‡#);
+ ##[ napply f_closed; nassumption ##| alias symbol "refl" = "refl1".
+napply (. E‡#);
nwhd; napply f_closed; nassumption]##]
#E'; ncut(i1 = i1'); ##[ napply (f_inj … E'); nassumption; ##]
#E''; nrewrite < E''; @;