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Proof step 8 from proof update-keyin (previous step)

∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- fv .1, fv .2]) ↔ r0 -- sk ∈ st, sk ∈ fv ', sk ∈ fis0

User applied rule structural induction

And obtained the following new goals

Proof step 7:
∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- (sk0 × val) .1, (sk0 × val) .2]) ↔ r0 -- sk ∈ st, sk ∈ (sk0 × val) ', sk ∈ fis0

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

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