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Proof step 16 from proof update-putfis-sw (conclusion)

⊦ update(r, fis[sk, val], st) = (update(r, fis, st)[r -- sk, val])

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, (sk × val) ', st) = st[r -- sk, val]
Proof step 2:
⊦ update(r, [], st) = st
Proof step 15:
∀ r, sk, val, st. update(r, fis0[sk, val], st) = (update(r, fis0, st)[r -- sk, val]) ⊦ update(r, (fv + fis0)[sk, val], st) = (update(r, fv + fis0, st)[r -- sk, val])

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ [][sk, val] = (sk × val) '])]]