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Mirrors > Home > MPE Home > Th. List > clwwlkfv | Structured version Visualization version GIF version |
Description: Lemma 2 for clwwlkf1o 29044: the value of function πΉ. (Contributed by Alexander van der Vekens, 28-Sep-2018.) (Revised by AV, 26-Apr-2021.) (Revised by AV, 1-Nov-2022.) |
Ref | Expression |
---|---|
clwwlkf1o.d | β’ π· = {π€ β (π WWalksN πΊ) β£ (lastSβπ€) = (π€β0)} |
clwwlkf1o.f | β’ πΉ = (π‘ β π· β¦ (π‘ prefix π)) |
Ref | Expression |
---|---|
clwwlkfv | β’ (π β π· β (πΉβπ) = (π prefix π)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 7368 | . 2 β’ (π‘ = π β (π‘ prefix π) = (π prefix π)) | |
2 | clwwlkf1o.f | . 2 β’ πΉ = (π‘ β π· β¦ (π‘ prefix π)) | |
3 | ovex 7394 | . 2 β’ (π prefix π) β V | |
4 | 1, 2, 3 | fvmpt 6952 | 1 β’ (π β π· β (πΉβπ) = (π prefix π)) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 = wceq 1542 β wcel 2107 {crab 3406 β¦ cmpt 5192 βcfv 6500 (class class class)co 7361 0cc0 11059 lastSclsw 14459 prefix cpfx 14567 WWalksN cwwlksn 28820 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5260 ax-nul 5267 ax-pr 5388 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-opab 5172 df-mpt 5193 df-id 5535 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-iota 6452 df-fun 6502 df-fv 6508 df-ov 7364 |
This theorem is referenced by: clwwlkf1 29042 clwwlkfo 29043 |
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