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Mirrors > Home > MPE Home > Th. List > erclwwlkrel | Structured version Visualization version GIF version |
Description: ∼ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by AV, 29-Apr-2021.) |
Ref | Expression |
---|---|
erclwwlk.r | ⊢ ∼ = {〈𝑢, 𝑤〉 ∣ (𝑢 ∈ (ClWWalks‘𝐺) ∧ 𝑤 ∈ (ClWWalks‘𝐺) ∧ ∃𝑛 ∈ (0...(♯‘𝑤))𝑢 = (𝑤 cyclShift 𝑛))} |
Ref | Expression |
---|---|
erclwwlkrel | ⊢ Rel ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | erclwwlk.r | . 2 ⊢ ∼ = {〈𝑢, 𝑤〉 ∣ (𝑢 ∈ (ClWWalks‘𝐺) ∧ 𝑤 ∈ (ClWWalks‘𝐺) ∧ ∃𝑛 ∈ (0...(♯‘𝑤))𝑢 = (𝑤 cyclShift 𝑛))} | |
2 | 1 | relopabi 5697 | 1 ⊢ Rel ∼ |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1083 = wceq 1536 ∈ wcel 2113 ∃wrex 3142 {copab 5131 Rel wrel 5563 ‘cfv 6358 (class class class)co 7159 0cc0 10540 ...cfz 12895 ♯chash 13693 cyclShift ccsh 14153 ClWWalkscclwwlk 27762 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-rab 3150 df-v 3499 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-if 4471 df-sn 4571 df-pr 4573 df-op 4577 df-opab 5132 df-xp 5564 df-rel 5565 |
This theorem is referenced by: erclwwlk 27804 |
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