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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > grlimdmrel | Structured version Visualization version GIF version |
Description: The domain of the graph local isomorphism function is a relation. (Contributed by AV, 20-May-2025.) |
Ref | Expression |
---|---|
grlimdmrel | ⊢ Rel dom GraphLocIso |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-grlim 47881 | . 2 ⊢ GraphLocIso = (𝑔 ∈ V, ℎ ∈ V ↦ {𝑓 ∣ (𝑓:(Vtx‘𝑔)–1-1-onto→(Vtx‘ℎ) ∧ ∀𝑣 ∈ (Vtx‘𝑔)(𝑔 ISubGr (𝑔 ClNeighbVtx 𝑣)) ≃𝑔𝑟 (ℎ ISubGr (ℎ ClNeighbVtx (𝑓‘𝑣))))}) | |
2 | 1 | reldmmpo 7567 | 1 ⊢ Rel dom GraphLocIso |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 {cab 2712 ∀wral 3059 Vcvv 3478 class class class wbr 5148 dom cdm 5689 Rel wrel 5694 –1-1-onto→wf1o 6562 ‘cfv 6563 (class class class)co 7431 Vtxcvtx 29028 ClNeighbVtx cclnbgr 47743 ISubGr cisubgr 47784 ≃𝑔𝑟 cgric 47800 GraphLocIso cgrlim 47879 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pr 5438 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-nf 1781 df-sb 2063 df-mo 2538 df-eu 2567 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-br 5149 df-opab 5211 df-xp 5695 df-rel 5696 df-dm 5699 df-oprab 7435 df-mpo 7436 df-grlim 47881 |
This theorem is referenced by: grlimprop 47887 grlimprop2 47889 grlicrcl 47903 grilcbri2 47907 |
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