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Proof step 17 from proof pathex-put-last (previous step)

path∃(str, r, r0, st[r0 -- sk, val]) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ r0 → (path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r -- _type] .type, st)))
Proof step 2:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 16:
r ≠ r0, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ ¬ dups(refs) ∧ validrefs(str, refs, (st[r0 -- sk, val][r -- _type]) .type, st[r0 -- sk, val]) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st)

Rule argument

[crewrite-arg: pathex-def-nodups , F , [st, r0, r, str] → [st[r0 -- sk, val], r0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)])], [EXTRATERMS : (st[r0 -- sk, val], r0, r, str)]]