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Mirrors > Home > MPE Home > Th. List > lencl | Structured version Visualization version GIF version |
Description: The length of a word is a nonnegative integer. This corresponds to the definition in Section 9.1 of [AhoHopUll] p. 318. (Contributed by Stefan O'Rear, 27-Aug-2015.) |
Ref | Expression |
---|---|
lencl | ⊢ (𝑊 ∈ Word 𝑆 → (♯‘𝑊) ∈ ℕ0) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wrdfin 14087 | . 2 ⊢ (𝑊 ∈ Word 𝑆 → 𝑊 ∈ Fin) | |
2 | hashcl 13923 | . 2 ⊢ (𝑊 ∈ Fin → (♯‘𝑊) ∈ ℕ0) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝑊 ∈ Word 𝑆 → (♯‘𝑊) ∈ ℕ0) |
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