Hi, I encountered a few issues in the Metamath problem statements:
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$( |
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@{ |
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amc12a-2002-p21.0 @e |- ( ph -> U : NN --> NN0 ) $@ |
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amc12a-2002-p21.1 @e |- ( ph -> ( U ` 1 ) = 4 ) $@ |
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amc12a-2002-p21.2 @e |- ( ph -> ( U ` 2 ) = 7 ) $@ |
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amc12a-2002-p21.3 @e |- ( ph -> A. n e. ( ZZ>= ` 3 ) ( U ` ( n + 2 ) ) = ( ( ( U ` n ) + ( U ` ( n + 1 ) ) ) mod 10 ) ) $@ |
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@( (Contributed by Kunhao Zheng, 4-May-2021.) @) |
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amc12a-2002-p21 @p |- ( ph -> ( A. n e. NN sum_ k e. ( 1 ... N ) ( U ` k ) > ; ; ; ; 1 0 0 0 0 -> ; ; ; 1 9 9 9 <_ n ) ) @= |
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? @. |
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@} |
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$) |
where 10 in L6 is an unknown token. It should be corrected to ; 1 0.
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$( |
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@{ |
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aime-1983-p1.0 @e |- ( ph -> X e. NN ) $@ |
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aime-1983-p1.1 @e |- ( ph -> Y e. NN ) $@ |
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aime-1983-p1.2 @e |- ( ph -> Z e. NN ) $@ |
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aime-1983-p1.3 @e |- ( ph -> 1 < X ) $@ |
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aime-1983-p1.4 @e |- ( ph -> 1 < Y ) $@ |
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aime-1983-p1.5 @e |- ( ph -> 1 < Z ) $@ |
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aime-1983-p1.6 @e |- ( ph -> W e. NN0 ) $@ |
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aime-1983-p1.7 @e |- ( ph -> ( X logb W ) = ; 2 4 ) $@ |
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aime-1983-p1.8 @e |- ( ph -> ( Y logb W ) = ; 4 0 ) $@ |
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aime-1983-p1.9 @e |- ( ph -> ( ( X x. ( Y x. Z ) ) logb W ) = ; 1 2 ) $@ |
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$@ (Contributed by Kudzo Ahegbebu, 28-Jun-2021.) $@ |
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aime-1983-p1 @p |- ( ph -> ( Z logb W ) = ; 6 0 ) @= |
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? @. |
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@} |
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$) |
where $@ in L13 is incorrectly used for comments. According to the convention in other problems, it should be @( and @).
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$( |
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@{ |
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aime-1994-p3.0 @e |- ( ph -> X e. RR ) $@ |
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aime-1994-p3.1 @e |- ( ph -> F : RR --> RR ) $@ |
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aime-1994-p3.2 @e |- ( ph -> ( ( F ` X ) + ( F ` ( X + 1 ) ) ) = ( X ^ 2 ) ) $@ |
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aime-1994-p3.3 @e |- ( ph -> ( F ` ; 1 9 ) = ; 9 4 ) $@ |
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@( (Contributed by Kudzo Ahegbebu, 28-Jun-2021.) @) |
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aime-1994-p3.3 @p |- ( ph -> ( ( F ` ; 9 4 ) mod ; ; ; 1 0 0 0 ) = ; ; 5 6 1 ) @= |
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? @. |
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@} |
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$) |
where aime-1994-p3.3 is multiply defined. It should be standardized to aime-1994-p3 as per Metamath conventions.
