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Proof step 2 from proof at-put-first-06 (conclusion)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sks0 ≠ [] → (st[r -- (sk ' + sk0 '), val][st[r -- sk] .refval -- (sk0 ' + sks0)]) = (st[r -- (sk ' + sk0 '), val][val .refval -- sks0])

Rule argument

[crewrite-arg: at-put-first-04 , F , [sks0, val, sk0, sk, r, st] → [sk1 ' + sks, val, sk0, sk, r, st] ]

Additional information

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