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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 3878 | . . 3 ⊢ ¬ 〈𝑊, (R1𝑑)〉 ∈ ∅ | |
2 | df-br 4584 | . . 3 ⊢ (𝑊∅(R1𝑑) ↔ 〈𝑊, (R1𝑑)〉 ∈ ∅) | |
3 | 1, 2 | mtbir 312 | . 2 ⊢ ¬ 𝑊∅(R1𝑑) |
4 | 3 | intnan 951 | 1 ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∧ wa 383 ∈ wcel 1977 ∅c0 3874 〈cop 4131 class class class wbr 4583 (class class class)co 6549 Rcnr 9566 0cc0 9815 1c1 9816 |
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-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-nul 3875 df-br 4584 |
This theorem is referenced by: (None) |
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