Theorem relqmap

Description: Quotient map is a relation. Guarantees that QMap can be composed, restricted, and used in other relation infrastructure (e.g., membership in Disjs , Rels -based typing). (Contributed by Peter Mazsa, 12-Feb-2026)

	Ref	Expression
Assertion	relqmap	|- Rel QMap R

Proof

Step	Hyp	Ref	Expression
1		mptrel	|- Rel ( x e. dom R |-> [ x ] R )
2		df-qmap	|- QMap R = ( x e. dom R |-> [ x ] R )
3	2	releqi	|- ( Rel QMap R <-> Rel ( x e. dom R |-> [ x ] R ) )
4	1 3	mpbir	|- Rel QMap R