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Proof step 7 from proof getkeys-app (conclusion)

⊦ (fis + fis0) .keys = fis .keys + fis0 .keys

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ [] .keys = []
Proof step 6:
∀ fis0. (fis1 + fis0) .keys = fis1 .keys + fis0 .keys ⊦ ((fv + fis1) + fis0) .keys = (fv + fis1) .keys + fis0 .keys

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ [] + fis = fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ [] + sks = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]