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Proof step 8 from proof add-put-switch (previous step)

is_fskey(sk), 0 ≤ i1, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i1 + 1) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i1, st[r0 -- sk, val0])[r0 -- i1 ', val]) = (addarray(r0, val, i1, st)[r0 -- i1 ', val][r0 -- sk, val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 7:
r0 -- sk ≠ r0 -- i1 ', is_fskey(sk), 0 ≤ i1, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i1 + 1) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i1, st[r0 -- sk, val0])[r0 -- i1 ', val]) = (addarray(r0, val, i1, st)[r0 -- sk, val0][r0 -- i1 ', val])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val0, r0 -- sk, val, r0 -- i1 ', addarray(r0, val, i1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')])], [EXTRATERMS : (val0, r0 -- sk, val, r0 -- i1 ', addarray(r0, val, i1, st))]]