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Metamath Proof Explorer

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 Could not format assertion : No typesetting found for |- Rel QMap R with typecode |-

Proof

Step Hyp Ref Expression
1 mptrel ⊢ Rel ⁡ x ∈ dom ⁡ R ⟼ x R
2 df-qmap Could not format QMap R = ( x e. dom R |-> [ x ] R ) : No typesetting found for |- QMap R = ( x e. dom R |-> [ x ] R ) with typecode |-
3 2 releqi Could not format ( Rel QMap R <-> Rel ( x e. dom R |-> [ x ] R ) ) : No typesetting found for |- ( Rel QMap R <-> Rel ( x e. dom R |-> [ x ] R ) ) with typecode |-
4 1 3 mpbir Could not format Rel QMap R : No typesetting found for |- Rel QMap R with typecode |-