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Proof step 6 from proof keys-in (previous step)

∀ sk. sk ∈ fis0 .keys ↔ sk ∈ fis0 ⊦ sk = fv .1 ∨ sk ∈ fis0 .keys ↔ sk ∈ fv ' ∨ sk ∈ fis0

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ sk. sk ∈ fis0 .keys ↔ sk ∈ fis0 ⊦ sk = (sk0 × val) .1 ∨ sk ∈ fis0 .keys ↔ sk ∈ (sk0 × val) ' ∨ sk ∈ fis0

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldvalue generated by ×;])]]