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verify/set

verify a relation between two sets

 Calling Sequence verify(expr1, expr2, set) verify(expr1, expr2, set(ver))

Parameters

 expr1, expr2 - anything, assumed to be of type set ver - verification for the set operands

Description

 • The verify(expr1, expr2, set) and verify(expr1, expr2, set(ver)) calling sequences return true if for every operand x in the first set, expr1, it can be determined that there is an operand y in the second set, expr2, that satisfies the relationship verify(x, y, ver), and similarly for every y in expr2 there must be an x in expr1 satisfying verify(x, y, ver). If ver is not given, then equality is used for the relationship.
 • If true is returned, then it has been determined that each operand of each set satisfies the relationship with at least one element in the other set. If false is returned, then there is at least one operand in one of the sets that does not satisfy the relationship (a result of type verify(false)) with all the elements in the other set, and otherwise FAIL.
 • The verification set is symmetric. The verification set(ver) is symmetric if and only if the verification ver is symmetric.
 • If either expr1 or expr2 is not of type set, then false is returned.

Examples

 > $\mathrm{verify}\left(\left\{a,b,x\left(x-1\right)\right\},\left\{a,b,{x}^{2}-x\right\},'\mathrm{set}'\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{verify}\left(\left\{a,b,x\left(x-1\right)\right\},\left\{a,b,{x}^{2}-x\right\},'\mathrm{set}'\left('\mathrm{expand}'\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{verify}\left(\left\{0.32,0.532,0.723\right\},\left\{0.23,0.33,0.65\right\},'\mathrm{set}'\left('\mathrm{less_than}'\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{verify}\left(\left\{0.23,0.33,0.65\right\},\left\{0.32,0.532,0.723\right\},'\mathrm{set}'\left('\mathrm{less_than}'\right)\right)$
 ${\mathrm{true}}$ (4)