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Proof step 6 from proof nopathex-update (previous step)

_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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ sk ∈ fis ↔ (∃ val, fis0, fis1. fis = fis0 + (sk × val) ' + fis1)
Proof step 5:
∃ val, fis2, fis1. fis0 = fis2 + (_type × val) ' + fis1, 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: ,sk ∈ fis ↔ (∃ val, fis0, fis1. fis = fis0 + (sk × val) ' + fis1) ,[fis, sk] → [fis0, _type] ,F ,assoclist ,fieldinit ,ex ]

Additional information

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