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Proof step 4 from proof keys-empty (previous step)

fis .keys = [] ⊦ fis = []

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ (fis + fis0) .keys = fis .keys + fis0 .keys
Proof step 3:
⊦ fv ' .keys = fv .1 '

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ sk ' ≠ []], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]