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Proof step 20 from proof nopathex-update (previous step)

path∃(str, r, r0, update(r0, (sk × val) ' + fis, st)), ∀ str0, r1, r2, st0. path∃(str0, r1, r2, update(r2, fis, st0)) → junkref(str0, r1, st0) ∨ path∃(str0, r1, r2, st0) ⊦ _type = sk, _type ∈ fis, junkref(str, r, st), path∃(str, r, r0, st), dups(fis .keys), sk ∈ fis .keys

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 19:
path∃(str, r, r0, update(r0, fis, st)[r0 -- sk, val]), ∀ str0, r1, r2, st0. path∃(str0, r1, r2, update(r2, fis, st0)) → junkref(str0, r1, st0) ∨ path∃(str0, r1, r2, st0) ⊦ _type = sk, _type ∈ fis, junkref(str, r, st), path∃(str, r, r0, st), dups(fis .keys), sk ∈ fis .keys

Rule argument

[speclemmaarg: , update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val]) ,[st, fis, val, sk, r] → [st, fis, val, sk, r0] ,F ,okfuns , ,update-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis, val, sk, r0)]]