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Proof step 109 from proof junkrefs-union-disjoint (previous step)

is_array(str, r, st1 ∪ st) ∧ (st1 ∪ st)[r -- _type] .type ≤ ty, st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), r0 ' + acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st1 ∪ st)[r -- _length] .intval ∧ is_referencevalue((st1 ∪ st)[r -- i ']) ∧ (r0 ' + acc) .first = (st1 ∪ st)[r -- i '] .refval ∧ junkrefs(str, r0 ' + acc, (st1 ∪ st)[r -- _type] .type .type, st1 ∪ st)), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
st1 .refs ∩ st .refs = ∅, 0 < (st1 ∪ st)[r -- _length] .intval, 0 ≤ i, st1[r -- _type] .type ≤ ty, r ∈ st1, junkrefs(str, (st1 ∪ st)[r -- i '] .refval ' + acc, (st1 ∪ st)[r -- _type] .type .type, st1 ∪ st), is_referencevalue((st1 ∪ st)[r -- i ']), i < (st1 ∪ st)[r -- _length] .intval, is_array(str, r, st1), (st1 ∪ st)[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st1[r -- i0 ']) ∧ (st1 ∪ st)[r -- i '] .refval = st1[r -- i0 '] .refval ∧ junkrefs(str, st1[r -- i0 '] .refval ' + acc, st1[r -- _type] .type .type, st1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ is_array(str, r, st1) → is_array(str, r, st1 ∪ st)], [CSIMPSEQ : ⊦ rset ∩ rset0 = rset0 ∩ rset], [CSIMPSEQ : ⊦ (rset ∩ rset0) ∩ rset1 = rset ∩ rset0 ∩ rset1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])]]