23 lines
1.0 KiB
Python
23 lines
1.0 KiB
Python
# Perform the proofs under the assumption that n is a nonnegative integer input constant. n stands
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# for the total number of input sets
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input: n -> integer.
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assume: n >= 0.
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# s/2 is the input predicate defining the sets for which the program searches for exact covers
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input: s/2.
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# Only the in/1 predicate is an actual output, s/2 is an input and covered/1 and is_int/1 are
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# auxiliary
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output: in_cover/1.
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# Perform the proofs under the assumption that the second parameter of s/2 (the number of the set)
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# is always an integer
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assume: forall Y (exists X s(X, Y) -> exists I (Y = I and I >= 1 and I <= n)).
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# Only valid sets can be included in the solution
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spec: forall Y (in_cover(Y) -> exists I (Y = I and I >= 1 and I <= n)).
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# If an element is contained in an input set, it must be covered by all solutions
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spec: forall X (exists Y s(X, Y) -> exists Y (s(X, Y) and in_cover(Y))).
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# Elements may not be covered by two input sets
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spec: forall Y, Z (exists X (s(X, Y) and s(X, Z)) and in_cover(Y) and in_cover(Z) -> Y = Z).
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