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Proof step 11 from proof put-put-switch (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sks ≠ [] → st[r -- (sk ' + sks), val] = st[st[r -- sk] .refval -- sks, val]
Proof step 5:
¬ sks ≠ [], sks = [] ∨ (∀ st, r, sk, val, r0, val0. (st[r -- sk, val][r0 -- sks, val0]) = (st[r0 -- sks, val0][r -- sk, val]) ∨ sk ∈ sks) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks), val0]) = (st[r0 -- (sk0 ' + sks), val0][r -- sk, val]), sk = sk0, sk ∈ sks
Proof step 10:
sks ≠ [], sks = [] ∨ (∀ st, r, sk, val, r0, val0. (st[r -- sk, val][r0 -- sks, val0]) = (st[r0 -- sks, val0][r -- sk, val]) ∨ sk ∈ sks) ⊦ (st[r -- sk, val][(st[r -- sk, val][r0 -- sk0]) .refval -- sks, val0]) = (st[r0 -- (sk0 ' + sks), val0][r -- sk, val]), sk = sk0, sk ∈ sks

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val0, sks, sk0, r0, st[r -- sk, val])]]