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Mirrors > Home > MPE Home > Th. List > helloworld | Structured version Visualization version GIF version |
Description: The classic "Hello world" benchmark has been translated into 314 computer programming languages - see http://www.roesler-ac.de/wolfram/hello.htm. However, for many years it eluded a proof that it is more than just a conjecture, even though a wily mathematician once claimed, "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." Using an IBM 709 mainframe, a team of mathematicians led by Prof. Loof Lirpa, at the New College of Tahiti, were finally able put it rest with a remarkably short proof only 4 lines long. (Contributed by Prof. Loof Lirpa, 1-Apr-2007.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
helloworld | ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 4296 | . . 3 ⊢ ¬ 〈𝑊, (R1𝑑)〉 ∈ ∅ | |
2 | df-br 5060 | . . 3 ⊢ (𝑊∅(R1𝑑) ↔ 〈𝑊, (R1𝑑)〉 ∈ ∅) | |
3 | 1, 2 | mtbir 325 | . 2 ⊢ ¬ 𝑊∅(R1𝑑) |
4 | 3 | intnan 489 | 1 ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∧ wa 398 ∈ wcel 2110 ∅c0 4291 〈cop 4567 class class class wbr 5059 (class class class)co 7150 Rcnr 10281 0cc0 10531 1c1 10532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-dif 3939 df-nul 4292 df-br 5060 |
This theorem is referenced by: (None) |
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