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Proof step 43 from proof junkrefs-put-nopathex-equiv (previous step)

is_array(str, r1, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r1 -- _type]) .type ≤ ty, st[r1 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), i < st[r1 -- _length] .intval, is_valid_ref(str, r0, st), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), 0 < st[r1 -- _length] .intval, 0 ≤ i, ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ sk = _type, r1 = jvmref, r0 = r1, r2 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r0 -- sk, val][r1 -- _length]) .intval ∧ is_referencevalue(st[r0 -- sk, val][r1 -- i ']) ∧ (r2 ' + refs) .first = (st[r0 -- sk, val][r1 -- i ']) .refval ∧ junkrefs(str, r2 ' + refs, (st[r0 -- sk, val][r1 -- _type]) .type .type, st[r0 -- sk, val])), path∃(str, r1, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
st[r1 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), i < st[r1 -- _length] .intval, is_valid_ref(str, r0, st), 0 < st[r1 -- _length] .intval, 0 ≤ i, is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ sk = _type, r1 = jvmref, r0 = r1, path∃(str, r1, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))])]]