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Proof step 7 from proof update-ex-nodups (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,fis ⊆ fis0 ↔ (∀ fv. fv ∈ fis → fv ∈ fis0) ,[fis0, fis] → [(sk × val) ' + fis0, fis[sk, val]] ,F ,list-set ,fieldinit-assoclista ,subset ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ fv ∈ fv0 ' + fis ↔ fv ≠ fv0 ∧ ¬ fv ∈ fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPFORWARD : ⊦ fis ⊆ fis0 ∧ ¬ fv ∈ fis0 → ¬ fv ∈ fis], [CSIMPSEQ : ⊦ ¬ fv ∈ fis → ( fv ∈ fis[sk, val] ↔ fv = sk × val)])], [EXTRATERMS : ((sk × val) ' + fis0, fis[sk, val])]]