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MM> READ "min_found.mm" | ||
Reading source file "min_found.mm"... 775 bytes | ||
775 bytes were read into the source buffer. | ||
The source has 18 statements; 5 are $a and 2 are $p. | ||
SET EMPTY_SUBSTITUTION was turned ON (allowed) for this database. | ||
No errors were found. However, proofs were not checked. Type VERIFY PROOF * | ||
if you want to check them. | ||
MM> Continuous scrolling is now in effect. | ||
MM> 0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% | ||
.................................................. | ||
All proofs in the database were verified in x.xx s. | ||
MM> Entering the Proof Assistant. HELP PROOF_ASSISTANT for help, EXIT to exit. | ||
You will be working on statement (from "SHOW STATEMENT th2"): | ||
18 th2 $p D $= ... $. | ||
Note: The proof you are starting with is already complete. | ||
MM-PA> Bytes refer to compressed proof size, steps to uncompressed length. | ||
Scanning forward through statements... | ||
Proof of "th2" decreased from 24 to 15 bytes using "in1". | ||
Scanning backward through statements... | ||
Proof of "th2" decreased from 24 to 15 bytes using "in1". | ||
The forward scan results were used. | ||
MM-PA> Proof of "th2": | ||
---------Clip out the proof below this line to put it in the source file: | ||
( ax-1 in1 ) AB $. | ||
---------The proof of "th2" (15 bytes) ends above this line. | ||
MM-PA> EXIT | ||
Warning: You have not saved changes to the proof of "th2". | ||
Do you want to EXIT anyway (Y, N) <N>? Y | ||
Exiting the Proof Assistant. Type EXIT again to exit Metamath. |
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verify proof * | ||
prove th2 | ||
minimize * /allow * | ||
show new /compressed |
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$( A shortening found by the minimizer. The comparison with min-not-found.mm | ||
suggests that the minimizer's ability to detect this one depends on the | ||
presence of statement "A" in at least one of the steps of the minimized | ||
proof. Axiom ax-3 and costant C are not used here, but they are kept | ||
anyway to lessen the amount of differences with min-found.mm. $) | ||
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$c A B C D $. | ||
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ax-1 $a A $. | ||
ax-2 $a B $. | ||
ax-3 $a C $. | ||
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${ | ||
in1.1 $e A $. | ||
in1 $a D $. | ||
$} | ||
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${ | ||
in2.1 $e B $. | ||
in2.2 $e A $. | ||
in2.3 $e B $. | ||
in2.4 $e B $. | ||
in2.5 $e B $. | ||
in2 $a D $. | ||
$} | ||
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$( Minimized proof, found automatically. (New usage is discouraged.) $) | ||
th1 $p D $= ( ax-1 in1 ) AB $. | ||
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$( Non-minimized proof. $) | ||
th2 $p D $= ( ax-2 ax-1 in2 ) ABAAAC $. |
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MM> READ "min_not_found.mm" | ||
Reading source file "min_not_found.mm"... 762 bytes | ||
762 bytes were read into the source buffer. | ||
The source has 18 statements; 5 are $a and 2 are $p. | ||
SET EMPTY_SUBSTITUTION was turned ON (allowed) for this database. | ||
No errors were found. However, proofs were not checked. Type VERIFY PROOF * | ||
if you want to check them. | ||
MM> Continuous scrolling is now in effect. | ||
MM> 0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% | ||
.................................................. | ||
All proofs in the database were verified in x.xx s. | ||
MM> Entering the Proof Assistant. HELP PROOF_ASSISTANT for help, EXIT to exit. | ||
You will be working on statement (from "SHOW STATEMENT th2"): | ||
18 th2 $p D $= ... $. | ||
Note: The proof you are starting with is already complete. | ||
MM-PA> Bytes refer to compressed proof size, steps to uncompressed length. | ||
Scanning forward through statements... | ||
No shorter proof was found. | ||
MM-PA> Proof of "th2": | ||
---------Clip out the proof below this line to put it in the source file: | ||
( ax-2 ax-3 in2 ) ABAAAC $. | ||
---------The proof of "th2" (24 bytes) ends above this line. | ||
MM-PA> EXIT | ||
Exiting the Proof Assistant. Type EXIT again to exit Metamath. |
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Original file line number | Diff line number | Diff line change |
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@@ -0,0 +1,4 @@ | ||
verify proof * | ||
prove th2 | ||
minimize * /allow * | ||
show new /compressed |
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Original file line number | Diff line number | Diff line change |
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$( A shortening not found by the minimizer. The comparison with min-found.mm | ||
suggests that the minimizer's inability to detect it is due to the absence | ||
of statement "C" in any of the steps of the minimized proof. The | ||
shortening is detected if proveFloating is set to 1 in minimizeProof, | ||
which allows absent "$e" statements to be found. $) | ||
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$c A B C D $. | ||
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ax-1 $a A $. | ||
ax-2 $a B $. | ||
ax-3 $a C $. | ||
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${ | ||
in1.1 $e A $. | ||
in1 $a D $. | ||
$} | ||
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${ | ||
in2.1 $e B $. | ||
in2.2 $e C $. | ||
in2.3 $e B $. | ||
in2.4 $e B $. | ||
in2.5 $e B $. | ||
in2 $a D $. | ||
$} | ||
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$( Minimized proof, not found automatically. (New usage is discouraged.) $) | ||
th1 $p D $= ( ax-1 in1 ) AB $. | ||
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$( Non-minimized proof. $) | ||
th2 $p D $= ( ax-2 ax-3 in2 ) ABAAAC $. |