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Proof step 25 from proof pathexplus-pathex (previous step)

st[(r ' + refs) .last -- _type] .type = mkarraytype(ty), is_array(str, (r ' + refs) .last, st), is_valid_ref(str, r, st), validrefs(str, r ' + refs + st[(r ' + refs) .last -- i '] .refval ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), i < st[(r ' + refs) .last -- _length] .intval, is_referencevalue(st[(r ' + refs) .last -- i ']), validrefs(str, st[(r ' + refs) .last -- i '] .refval ', ty, st), 0 ≤ i, 0 < st[(r ' + refs) .last -- _length] .intval ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = st[(r ' + refs) .last -- i '] .refval, ∃ i0. ¬ i0 < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i0 ∧ is_referencevalue(st[(r ' + refs) .last -- i0 ']) ∧ st[(r ' + refs) .last -- i0 '] .refval = st[(r ' + refs) .last -- i '] .refval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
st[(r ' + refs) .last -- i '] = refval(r0), st[(r ' + refs) .last -- _type] .type = mkarraytype(ty), is_array(str, (r ' + refs) .last, st), is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), i < st[(r ' + refs) .last -- _length] .intval, is_referencevalue(st[(r ' + refs) .last -- i ']), validrefs(str, r0 ', ty, st), 0 ≤ i, 0 < st[(r ' + refs) .last -- _length] .intval ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, ∃ i0. ¬ i0 < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i0 ∧ is_referencevalue(st[(r ' + refs) .last -- i0 ']) ∧ st[(r ' + refs) .last -- i0 '] .refval = r0

Rule argument

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

Additional information

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