![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > disjwrdpfx | Structured version Visualization version GIF version |
Description: Sets of words are disjoint if each set contains exactly the extensions of distinct words of a fixed length. Remark: A word 𝑊 is called an "extension" of a word 𝑃 if 𝑃 is a prefix of 𝑊. (Contributed by AV, 29-Jul-2018.) (Revised by AV, 6-May-2020.) |
Ref | Expression |
---|---|
disjwrdpfx | ⊢ Disj 𝑦 ∈ 𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 prefix 𝑁) = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | invdisjrab 5129 | 1 ⊢ Disj 𝑦 ∈ 𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 prefix 𝑁) = 𝑦} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 {crab 3419 Disj wdisj 5108 (class class class)co 7416 Word cword 14496 prefix cpfx 14652 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ral 3052 df-rmo 3364 df-rab 3420 df-v 3465 df-sbc 3769 df-csb 3885 df-disj 5109 |
This theorem is referenced by: disjxwwlksn 29759 disjxwwlkn 29768 |
Copyright terms: Public domain | W3C validator |