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Proof step 13 from proof add-put-switch (previous step)

is_fskey(sk) ⊦ addarray(r0, val, i, st[r0 -- sk, val0]) = (addarray(r0, val, i, st)[r0 -- sk, val0])

User applied rule induction

And obtained the following new goals

Proof step 12:
is_fskey(sk), ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ addarray(r0, val, i, st[r0 -- sk, val0]) = (addarray(r0, val, i, st)[r0 -- sk, val0])

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, i→n(i), [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (i→n(i))]]