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Proof step 13 from proof update-put-notin (previous step)

⊦ (update(r0, fis, st)[r -- sk, val]) = update(r0, fis, st[r -- sk, val]), sk ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ r0 → (update(r0, fis, st)[r -- sk, val]) = update(r0, fis, st[r -- sk, val])
Proof step 12:
¬ r ≠ r0 ⊦ (update(r0, fis, st)[r -- sk, val]) = update(r0, fis, st[r -- sk, val]), sk ∈ fis

Rule argument

[crewrite-arg: update-put , F , [val, sk, r, st, fis, r0] → [val, sk, r, st, fis, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, r, st, fis, r0)]]