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Proof step 2 from proof at-put-other-03 (conclusion)

⊦ (st[r -- i ', val][r0 -- (mkfs(class, ty, fieldvar) ' ' + mkfs(class0, ty0, fieldvar0) ' ')]) = st[r0 -- (mkfs(class, ty, fieldvar) ' ' + mkfs(class0, ty0, fieldvar0) ' ')]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ ¬ sk ∈ sks ∧ sks ≠ [] → (st[r -- sk, val][r0 -- sks]) = st[r0 -- sks]

Rule argument

[crewrite-arg: at-put-other-02 , F , [sks, r0, val, sk, r, st] → [mkfs(class, ty, fieldvar) ' ' + mkfs(class0, ty0, fieldvar0) ' ', r0, val, i ', r, st] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ sks + sks0 ↔ ¬ ¬ (sk ∈ sks ∨ sk ∈ sks0)], [CSIMPSEQ : ⊦ sk ∈ sk0 ' ↔ sk = sk0], [CSIMPSEQ : ⊦ fs ' ≠ i '], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ sk ' ≠ []])], [EXTRATERMS : ( mkfs(class, ty, fieldvar) ' ' + mkfs(class0, ty0, fieldvar0) ' ', r0, val, i ', r, st)]]