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Proof step 7 from proof nopathex-update (previous step)

_type ∈ fis0, update(r0, fis, st) = update(r0, fis0, st), fis0 ⊆ fis, path∃(str, r, r0, update(r0, fis0, st)) ⊦ junkref(str, r, st), _type ∈ fis, path∃(str, r, r0, st), dups(fis0 .keys)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ fis ⊆ fis0 ↔ (∀ fv. fv ∈ fis → fv ∈ fis0)
Proof step 6:
_type ∈ fis0, update(r0, fis, st) = update(r0, fis0, st), ∀ fv. fv ∈ fis0 → fv ∈ fis, path∃(str, r, r0, update(r0, fis0, st)) ⊦ junkref(str, r, st), _type ∈ fis, path∃(str, r, r0, st), dups(fis0 .keys)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (fis, fis0)]]