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Proof step 8 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), ¬ path∃(str, r, r0, update(r0, fis0, st)) ∧ ¬ junkref(str, r, update(r0, fis0, st))

User applied rule case distinction

And obtained the following new goals

Proof step 5:
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) ⊦ ¬ path∃(str, r, r0, update(r0, fis0, st)), _type = sk, _type ∈ fis0, junkref(str, r, st), path∃(str, r, r0, st)
Proof step 7:
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) ⊦ ¬ junkref(str, r, update(r0, fis0, st)), _type = sk, _type ∈ fis0, junkref(str, r, st), path∃(str, r, r0, st)

Rule argument

[CASEDARG : pos: right 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]