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Proof step 3 from proof resetcnt-length (conclusion)

⊦ # resetcnt(P0) = # P0

User applied rule structural induction

And closed the goal!

Rule argument

indvar:P0

Additional information

[Concretesimprules((Csimpnamedseq(resetcnt-empty,,, ⊦ resetcnt([]) = []) Csimpnamedseq(resetcnt-rec,,, ⊦ resetcnt(p ' + P) = p.count:= 0 + resetcnt(P)) Csimpgen(partition freely generated by [], +;) Csimpnamedseq(list,partition,c, ⊦ p + P = p ' + P) Csimpnamedseq(list,partition,a, ⊦ (P + P0) + P1 = P + P0 + P1) Csimpnamedseq(list,partition,len, ⊦ #(P + P0) = # P + # P0) Csimpnamedseq(list,partition,len-02, ⊦ # p ' = 0 +1) Csimpnamedseq(nat-basic2,,eq-01, ⊦ m + n = m + n0 ↔ n = n0) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(list-data,partition,size-01, ⊦ # [] = 0)))]