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programming_framework
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graph TD
    DefFact("DefFact Factorial")
    DefSum("DefSum Sum principle")
    DefProd("DefProd Product principle")
    PermNoRep("PermNoRep Permutations no rep")
    PermRep("PermRep Permutations with rep")
    CombNoRep("CombNoRep Combinations")
    CombRep("CombRep Combinations with rep")
    BinomThm("BinomThm Binomial theorem")
    Pascal("Pascal Pascal identity")
    Pigeonhole("Pigeonhole Pigeonhole principle")
    InclExcl("InclExcl Inclusion-exclusion")
    InclExcl3("InclExcl3 Incl-excl 3 sets")
    Derange("Derange Derangements")
    Stirling2("Stirling2 Stirling numbers")
    DefFact --> PermNoRep
    DefProd --> PermNoRep
    DefProd --> PermRep
    PermNoRep --> CombNoRep
    DefFact --> CombNoRep
    CombNoRep --> CombRep
    CombNoRep --> BinomThm
    CombNoRep --> Pascal
    DefSum --> Pigeonhole
    DefSum --> InclExcl
    InclExcl --> InclExcl3
    InclExcl --> Derange
    PermNoRep --> Derange
    DefSum --> Stirling2
    DefProd --> Stirling2
    classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b
    classDef definition fill:#3498db,color:#fff,stroke:#2980b9
    classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085
    class DefFact,DefSum,DefProd definition
    class PermNoRep,PermRep,CombNoRep,CombRep,BinomThm,Pascal,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem