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Proof step 12 from proof add-put-switch (previous step)

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])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 3:
⊦ i ≤ 0 → addarray(r, val, i, st) = st
Proof step 11:
i > 0, 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 - 1, st[r0 -- sk, val0])[r0 -- (i - 1) ', val]) = (addarray(r0, val, i, st)[r0 -- sk, val0])

Rule argument

[crewrite-arg: addarray-rec , F , [st, i, val, r] → [st[r0 -- sk, val0], i, val, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (st[r0 -- sk, val0], i, val, r0)]]