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Proof step 26 from proof pathexplus-pathex (previous step)

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

And obtained the following new goals

Proof step 25:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))])]]