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Proof step 9 from proof put-put-switch (previous step)

∀ st, r, sk, val, r0, val0. (st[r -- sk, val][r0 -- sks, val0]) = (st[r0 -- sks, val0][r -- sk, val]) ∨ sk ∈ sks ⊦ sk = sk0, sks = [], (st[r -- sk, val][st[r0 -- sk0] .refval -- sks, val0]) = (st[r0 -- (sk0 ' + sks), val0][r -- sk, val]), sk ∈ sks

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ sks ≠ [] → st[r -- (sk ' + sks), val] = st[st[r -- sk] .refval -- sks, val]
Proof step 8:
sks ≠ [], ∀ st, r, sk, val, r0, val0. (st[r -- sk, val][r0 -- sks, val0]) = (st[r0 -- sks, val0][r -- sk, val]) ∨ sk ∈ sks ⊦ sk = sk0, sks = [], (st[r -- sk, val][st[r0 -- sk0] .refval -- sks, val0]) = (st[st[r0 -- sk0] .refval -- sks, val0][r -- sk, val]), sk ∈ sks

Rule argument

[crewrite-arg: put-rec-01 , F , [val, sks, sk, r, st] → [val0, sks, sk0, r0, st] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val0, sks, sk0, r0, st)]]