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Proof step 9 from proof update-ex-nodups (previous step)

update(r, fis0, st) = update(r, fis, st), fis ⊆ fis0 ⊦ dups(fis .keys), (update(r, fis, st)[r -- sk, val]) = update(r, fis[sk, val], st) ∧ fis[sk, val] ⊆ (sk × val) ' + fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ update(r, fis[sk, val], st) = (update(r, fis, st)[r -- sk, val])
Proof step 8:
update(r, fis0, st) = update(r, fis, st), fis ⊆ fis0 ⊦ dups(fis .keys), (update(r, fis, st)[r -- sk, val]) = (update(r, fis, st)[r -- sk, val]) ∧ fis[sk, val] ⊆ (sk × val) ' + fis0

Rule argument

[crewrite-arg: update-putfis-sw , F , [st, val, sk, fis, r] → [st, val, sk, fis, r] ]

Additional information

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