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Proof step 151 from proof pathex-put-nopathex (previous step)

refs0 = [], is_array(str, r, st), refs0 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, st[r -- _type] .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, r = jvmref, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 147:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 150:
is_array(str, r, st), ∀ val, r0, sk, st, r, str, refs. # refs < # [] → ( 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, r = jvmref, junkref(str, r, st), path∃(str, r, r0, st), is_valid_ref(str, r, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs])]]