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	$⊢ R \in V \to (\forall u \in (dom R / R) \exists! t \in dom R u = [t] R \leftrightarrow \forall u \exists^{*} t \in dom R u = [t] R)$
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 \|-

Metamath Proof Explorer

Theorem disjqmap

Proof