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Proof step 3 from proof vals-length (conclusion)

⊦ # fis .vals = # fis

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ [] .vals = []
Proof step 2:
⊦ (fv ' + fis) .vals = fv .2 ' + fis .vals

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPNAMEDSEQ : list-data, fieldinit-assoclista, size-01, ⊦ # [] = 0], [CSIMPNAMEDSEQ : list-data, javavalues, size-01, ⊦ # [] = 0], [CSIMPNAMEDSEQ : list, fieldinit-assoclista, c, ⊦ fv + fis = fv ' + fis], [CSIMPNAMEDSEQ : list, fieldinit-assoclista, a, ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPNAMEDSEQ : list, javavalues, len, ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPNAMEDSEQ : list, javavalues, len-02, ⊦ # val ' = 0 +1], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list, fieldinit-assoclista, len, ⊦ # (fis + fis0) = # fis + # fis0], [CSIMPNAMEDSEQ : list, fieldinit-assoclista, len-02, ⊦ # fv ' = 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])]]