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Mirrors > Home > MPE Home > Th. List > disjxwrd | Structured version Visualization version GIF version |
Description: Sets of words are disjoint if each set contains extensions of distinct words of a fixed length. (Contributed by AV, 29-Jul-2018.) (Proof shortened by AV, 7-May-2020.) |
Ref | Expression |
---|---|
disjxwrd | ⊢ Disj 𝑦 ∈ 𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 substr 〈0, 𝑁〉) = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | invdisjrab 4572 | 1 ⊢ Disj 𝑦 ∈ 𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 substr 〈0, 𝑁〉) = 𝑦} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 {crab 2900 〈cop 4131 Disj wdisj 4553 (class class class)co 6549 0cc0 9815 Word cword 13146 substr csubstr 13150 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rmo 2904 df-rab 2905 df-v 3175 df-sbc 3403 df-csb 3500 df-disj 4554 |
This theorem is referenced by: disjxwwlks 26264 disjxwwlkn 26273 disjxwwlksn 41110 av-disjxwwlkn 41119 |
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