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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://helloworldcollection.de. 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 to put it to rest with a remarkably short proof only four 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 4235 | . . 3 ⊢ ¬ 〈𝑊, (R1𝑑)〉 ∈ ∅ | |
2 | df-br 5044 | . . 3 ⊢ (𝑊∅(R1𝑑) ↔ 〈𝑊, (R1𝑑)〉 ∈ ∅) | |
3 | 1, 2 | mtbir 326 | . 2 ⊢ ¬ 𝑊∅(R1𝑑) |
4 | 3 | intnan 490 | 1 ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∧ wa 399 ∈ wcel 2110 ∅c0 4227 〈cop 4537 class class class wbr 5043 (class class class)co 7202 Rcnr 10462 0cc0 10712 1c1 10713 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2706 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2713 df-cleq 2726 df-clel 2812 df-dif 3860 df-nul 4228 df-br 5044 |
This theorem is referenced by: (None) |
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