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Proof step 10 from proof junkref-update (previous step)

junkref(str, r, update(r0, fis0, st)[r0 -- sk, val]), ∀ str0, r1, r2, st0. junkref(str0, r1, update(r2, fis0, st0)) → path∃(str0, r1, r2, st0) ∨ junkref(str0, r1, st0) ⊦ _type = sk, _type ∈ fis0, junkref(str, r, st), path∃(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ path∃(str, r, r0, st) ∧ ¬ junkref(str, r, st) ∧ sk ≠ _type → ¬ junkref(str, r, st[r0 -- sk, val])
Proof step 9:
¬ (¬ path∃(str, r, r0, update(r0, fis0, st)) ∧ ¬ junkref(str, r, update(r0, fis0, st)) ∧ sk ≠ _type), junkref(str, r, update(r0, fis0, st)[r0 -- sk, val]), ∀ str0, r1, r2, st0. junkref(str0, r1, update(r2, fis0, st0)) → path∃(str0, r1, r2, st0) ∨ junkref(str0, r1, st0) ⊦ _type = sk, _type ∈ fis0, junkref(str, r, st), path∃(str, r, r0, st)

Rule argument

[crewrite-arg: junkref-put-nopathex , F , [val, sk, r0, st, r, str] → [val, sk, r0, update(r0, fis0, st), r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, r0, update(r0, fis0, st), r, str)]]