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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 Could not format assertion : No typesetting found for |- ( R AdjLiftMap A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 df-adjliftmap Could not format ( R AdjLiftMap A ) = QMap ( ( R u. `' _E ) |` A ) : No typesetting found for |- ( R AdjLiftMap A ) = QMap ( ( R u. `' _E ) |` A ) with typecode |-
2 df-qmap Could not format QMap ( ( R u. `' _E ) |` A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) ) : No typesetting found for |- QMap ( ( R u. `' _E ) |` A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) ) with typecode |-
3 1 2 eqtri Could not format ( R AdjLiftMap A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) ) : No typesetting found for |- ( R AdjLiftMap A ) = ( m e. dom ( ( R u. `' _E ) |` A ) |-> [ m ] ( ( R u. `' _E ) |` A ) ) with typecode |-