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Proof step 2 from proof update-rec-02 (previous step)

⊦ fis = [], update(r, fis, st) = (update(r, fis .rest, st)[r -- fis .first .1, fis .first .2])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1:
⊦ update(r, fv ' + fis, st) = (update(r, fis, st)[r -- fv .1, fv .2])

Rule argument

[speclemmaarg: fis ≠ [] ,fv = fis .first ∧ fis0 = fis .rest ↔ fis = fv + fis0 ,[fis, fv, fis0] → [fis, fv, fis0] ,T ,list-data ,fieldinit-assoclista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fv + fis = fv ' + fis], [CSIMPSEQ : ⊦ fv ' + fis ≠ []], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPELIM : fis ≠ [] ⊦ fv = fis .first ∧ fis0 = fis .rest ↔ fis = fv + fis0])], [EXTRATERMS : (fis, fv, fis0)]]