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Proof step 206 from proof pathex-put-nopathex (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st), r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 102:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 204:
r ≠ jvmref, validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st), r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st)
Proof step 205:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRATERMS : (st, st[r -- _type] .type, refs0, r, str)]]