ordered set inclusion

Question

Suppose I have a ordered set $A=\{2,3\}$ and $B=\{2,3,4\}$ and $C=\{2,4,3\}$. Is there any mathematica command whether $A\subset B$ gives true(or 1) but $A$ which is not a subset of $C$ gives false(or 0)?

I know OrderedQ, but that only gives OrderedQ[{2, 3}] == True and OrderedQ[{3, 2}] == False, so it was not that useful.

Answer 1

ClearAll[subsequenceQ]
subsequenceQ = MemberQ[Subsequences[#2, Length @ #], #] &;

Examples:

a = {2, 3} ; b = {2, 3, 4} ; c = {2, 4, 3};

subsequenceQ[a, b]

True

subsequenceQ[a, c]

False

subsequenceQ[a, {4, 2, 3, 5}]

True

Alternatively, you can use:

ClearAll[subsequenceQ1, subsequenceQ2, subsequenceQ3]

subsequenceQ1 = MemberQ[Partition[#2, Length@#, 1], #] &;

subsequenceQ2 = MatchQ[#2, Flatten[{___, #, ___}]] &;

subsequenceQ3 = SequenceCases[#2, #] =!= {} &;