Theorem disjqmap

Description: Disjointness of QMap equals unique generation of the quotient carrier. The cleaned, carrier-respecting version of disjqmap2 . This is the statement "each equivalence class has a unique representative" for the general coset carrier ( dom R /. R ) . (Contributed by Peter Mazsa, 12-Feb-2026)

	Ref	Expression
Assertion	disjqmap	Could not format assertion : No typesetting found for |- ( R e. V -> ( Disj QMap R <-> A. u e. ( dom R /. R ) E! t e. dom R u = [ t ] R ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		disjqmap2	Could not format ( R e. V -> ( Disj QMap R <-> A. u E* t e. dom R u = [ t ] R ) ) : No typesetting found for |- ( R e. V -> ( Disj QMap R <-> A. u E* t e. dom R u = [ t ] R ) ) with typecode |-
2		raldmqseu	$$⊢R\in V\to \left(\forall u\in \left(\mathrm{dom}R/R\right)\exists !t\in \mathrm{dom}Ru=\left[t\right]R\leftrightarrow \forall u{\exists }^{*}t\in \mathrm{dom}Ru=\left[t\right]R\right)$$
3	1 2	bitr4d	Could not format ( R e. V -> ( Disj QMap R <-> A. u e. ( dom R /. R ) E! t e. dom R u = [ t ] R ) ) : No typesetting found for |- ( R e. V -> ( Disj QMap R <-> A. u e. ( dom R /. R ) E! t e. dom R u = [ t ] R ) ) with typecode |-