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Proof step 2 from proof at-put-first-rec-02 (conclusion)

⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- (sk0 ' + sk1 ' + sks)]) = (st[r -- sk, val][st[r0 -- sk0] .refval -- (sk1 ' + sks)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sk ≠ sk0 ∧ sks ≠ [] → (st[r -- sk, val][r0 -- (sk0 ' + sks)]) = (st[r -- sk, val][st[r0 -- sk0] .refval -- sks])

Rule argument

[crewrite-arg: at-put-first-rec , F , [sks, sk0, r0, val, sk, r, st] → [sk1 ' + sks, sk0, r0, val, sk, r, st] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ sk ' ≠ []], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])], [EXTRATERMS : (sk1 ' + sks, sk0, r0, val, sk, r, st)]]