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Mirrors > Home > MPE Home > Th. List > erclwwlksrel | 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 |
---|---|
erclwwlks.r | ⊢ ∼ = {〈𝑢, 𝑤〉 ∣ (𝑢 ∈ (ClWWalks‘𝐺) ∧ 𝑤 ∈ (ClWWalks‘𝐺) ∧ ∃𝑛 ∈ (0...(#‘𝑤))𝑢 = (𝑤 cyclShift 𝑛))} |
Ref | Expression |
---|---|
erclwwlksrel | ⊢ Rel ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | erclwwlks.r | . 2 ⊢ ∼ = {〈𝑢, 𝑤〉 ∣ (𝑢 ∈ (ClWWalks‘𝐺) ∧ 𝑤 ∈ (ClWWalks‘𝐺) ∧ ∃𝑛 ∈ (0...(#‘𝑤))𝑢 = (𝑤 cyclShift 𝑛))} | |
2 | 1 | relopabi 5245 | 1 ⊢ Rel ∼ |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1037 = wceq 1483 ∈ wcel 1990 ∃wrex 2913 {copab 4712 Rel wrel 5119 ‘cfv 5888 (class class class)co 6650 0cc0 9936 ...cfz 12326 #chash 13117 cyclShift ccsh 13534 ClWWalkscclwwlks 26875 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-opab 4713 df-xp 5120 df-rel 5121 |
This theorem is referenced by: erclwwlks 26937 |
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