Metamath Proof Explorer

Theorem dfadjliftmap

Description: Alternate (expanded) definition of the adjoined lift map. (Contributed by Peter Mazsa, 28-Jan-2026) (Revised by Peter Mazsa, 22-Feb-2026)

Ref Expression
Assertion dfadjliftmap 
|- ( R AdjLiftMap A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) )

Proof

Step Hyp Ref Expression
1 df-adjliftmap 
 |-  ( R AdjLiftMap A ) = QMap ( ( R u. `' _E ) |` A )
2 df-qmap 
 |-  QMap ( ( R u. `' _E ) |` A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) )
3 1 2 eqtri 
 |-  ( R AdjLiftMap A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) )