Theorem dfblockliftmap 38630

Description: Alternate definition of the block lift map. (Contributed by Peter Mazsa, 29-Jan-2026.) (Revised by Peter Mazsa, 22-Feb-2026.)

Assertion

Ref	Expression
dfblockliftmap	⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

Distinct variable groups:   𝐴,𝑚   𝑅,𝑚

Proof of Theorem dfblockliftmap

Step	Hyp	Ref	Expression
1		df-blockliftmap 38629	. 2 ⊢ (𝑅 BlockLiftMap 𝐴) = QMap (𝑅 ⋉ (◡ E ↾ 𝐴))
2		df-qmap 38616	. 2 ⊢ QMap (𝑅 ⋉ (◡ E ↾ 𝐴)) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))
3	1, 2	eqtri 2758	1 ⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

Syntax hints:   = wceq 1542   ↦ cmpt 5178   E cep 5522  ^◡ccnv 5622  dom cdm 5623   ↾ cres 5625  [cec 8633   ⋉ cxrn 38344   QMap cqmap 38345   BlockLiftMap cblockliftmap 38347

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2727  df-qmap 38616  df-blockliftmap 38629

This theorem is referenced by:  dfblockliftmap2  38631