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Proof step 62 from proof validrefs-junkrefs (previous step)

st[r -- i '] = refval(r1), r1 ' + refs1 = refs + st[refs .last -- i0 '] .refval ' + refs0, 0 < st[refs .last -- _length] .intval, 0 ≤ i0, is_valid_ref(str, st[refs .last -- i0 '] .refval, st), r1 ∈ refs, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, validrefs(str, refs, st[r -- _type] .type .type, st), validrefs(str, r ' + refs, ty, st), is_referencevalue(st[refs .last -- i0 ']), i0 < st[refs .last -- _length] .intval, is_array(refs .last, st) ⊦ r = jvmref, st[refs .last -- i0 '] .refval = jvmref, refs = [], st[st[refs .last -- i0 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type, ∃ i1. ¬ i1 < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i1 ∧ is_referencevalue(st[refs .last -- i1 ']) ∧ st[refs .last -- i0 '] .refval = st[refs .last -- i1 '] .refval ∧ ¬ st[st[refs .last -- i1 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 61:
st[refs .last -- i0 '] = refval(r0), st[r -- i '] = refval(r1), r1 ' + refs1 = refs + r0 ' + refs0, 0 < st[refs .last -- _length] .intval, 0 ≤ i0, is_valid_ref(str, r0, st), r1 ∈ refs, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, validrefs(str, refs, st[r -- _type] .type .type, st), validrefs(str, r ' + refs, ty, st), is_referencevalue(st[refs .last -- i0 ']), i0 < st[refs .last -- _length] .intval, is_array(refs .last, st) ⊦ r = jvmref, r0 = jvmref, refs = [], st[r0 -- _type] .type ≤ st[refs .last -- _type] .type .type, ∃ i1. ¬ i1 < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i1 ∧ is_referencevalue(st[refs .last -- i1 ']) ∧ r0 = st[refs .last -- i1 '] .refval ∧ ¬ st[st[refs .last -- i1 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[refs .last -- i0 '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[refs .last -- i0 '], r0)]]