Theorem dfblockliftmap 39583

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 39582	. 2 ⊢ (𝑅 BlockLiftMap 𝐴) = QMap (𝑅 ⋉ (◡ E ↾ 𝐴))
2		df-qmap 39569	. 2 ⊢ QMap (𝑅 ⋉ (◡ E ↾ 𝐴)) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))
3	1, 2	eqtri 2786	1 ⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

This proof depends on syntax axioms:   = wceq 1570   ↦ cmpt 5189   E cep 5554  ^◡ccnv 5654  dom cdm 5655   ↾ cres 5657  [cec 8740   ⋉ cxrn 39297   QMap cqmap 39298   BlockLiftMap cblockliftmap 39300

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2755  df-qmap 39569  df-blockliftmap 39582

This theorem is used by:  dfblockliftmap2  39584