Theorem dfblockliftmap 38663

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 38662	. 2 ⊢ (𝑅 BlockLiftMap 𝐴) = QMap (𝑅 ⋉ (◡ E ↾ 𝐴))
2		df-qmap 38649	. 2 ⊢ QMap (𝑅 ⋉ (◡ E ↾ 𝐴)) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))
3	1, 2	eqtri 2760	1 ⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

Syntax hints:   = wceq 1542   ↦ cmpt 5180   E cep 5524  ^◡ccnv 5624  dom cdm 5625   ↾ cres 5627  [cec 8635   ⋉ cxrn 38377   QMap cqmap 38378   BlockLiftMap cblockliftmap 38380

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 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729  df-qmap 38649  df-blockliftmap 38662

This theorem is referenced by:  dfblockliftmap2  38664