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Proof step 10 from proof update-ex-nodups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ dups(fis[sk, val] .keys) ↔ dups(fis .keys)
Proof step 9:
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

Rule argument

[emptyarg]

Additional information

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