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Proof step 85 from proof pathex-put-nopathex (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 84:
refs0 .first = (st[r0 -- sk, val][r -- i ']) .refval, is_array(str, r, st[r0 -- sk, val]), i < (st[r0 -- sk, val][r -- _length]) .intval, is_referencevalue(st[r0 -- sk, val][r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st[r0 -- sk, val]), 0 ≤ i, 0 < (st[r0 -- sk, val][r -- _length]) .intval, ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st)) ⊦ sk = _type, r = jvmref, refs0 = [], junkref(str, r, st), path∃(str, r, r0, st), path∃(str, r, refs0 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])]]