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Fix the globality of an instance and simplify bfin_union a bit

This commit is contained in:
Dan Frumin 2017-09-24 18:34:35 +02:00
parent 206bf9edb6
commit bd91e18ad6
2 changed files with 6 additions and 13 deletions
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13
FiniteSets/subobjects/b_finite.v
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@ -409,16 +409,9 @@ Section kfin_bfin.
strip_truncations. strip_truncations.
revert fX. revert X. revert fX. revert X.
induction n; intros X fX. induction n; intros X fX.
- destruct HY as [m fY]. strip_truncations. - rewrite (X_empty _ X fX).
exists m. apply tr. rewrite (neutralL_max (Sub A)).
transitivity {a : A & a ∈ Y}; [ | assumption ]. apply HY.
apply equiv_functor_sigma_id.
intros a.
apply equiv_iff_hprop.
* intros Ha. strip_truncations.
destruct Ha as [Ha | Ha]; [ | apply Ha ].
contradiction (fX (a;Ha)).
* intros Ha. apply tr. by right.
- destruct (split X n fX) as - destruct (split X n fX) as
(X' & b & HX' & HX). (X' & b & HX' & HX).
assert (Bfin (X'∪ Y)) by (by apply IHn). assert (Bfin (X'∪ Y)) by (by apply IHn).

2
FiniteSets/subobjects/sub.v
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@ -24,7 +24,7 @@ Section sub_classes.
Variable C : (A -> hProp) -> hProp. Variable C : (A -> hProp) -> hProp.
Context `{Univalence}. Context `{Univalence}.
Instance subobject_lattice : Lattice (Sub A). Global Instance subobject_lattice : Lattice (Sub A).
Proof. Proof.
apply _. apply _.
Defined. Defined.