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Proof step 12 from proof init-switch (previous step)

is_fskey(sk) ⊦ addarray(r, vals, i, st[r0 -- sk, val]) = (addarray(r, vals, i, st)[r0 -- sk, val])

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ addarray(r, [], i, st) = st
Proof step 11:
∀ sk, r, i, st, r0, val. is_fskey(sk) → addarray(r, vals0, i, st[r0 -- sk, val]) = (addarray(r, vals0, i, st)[r0 -- sk, val]) ⊦ is_fskey(sk) → addarray(r, val + vals0, i, st[r0 -- sk, val0]) = (addarray(r, val + vals0, i, st)[r0 -- sk, val0])

Rule argument

[VARWITHFMAVARSARG : vals, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : javavalues generated by [], +;])]]