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Proof step 30 from proof pathexplus-pathex (previous step)

is_array(str, (r ' + refs) .last, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, 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) ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, is_classtype(st[(r ' + refs) .last -- _type] .type) ∧ (∃ fs. fs ' ∈ instfields(st[(r ' + refs) .last -- _type] .type .class) ∧ is_referencevalue(st[(r ' + refs) .last -- fs ']) ∧ st[(r ' + refs) .last -- fs '] .refval = r0), is_arraytype(st[(r ' + refs) .last -- _type] .type) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i ∧ is_referencevalue(st[(r ' + refs) .last -- i ']) ∧ st[(r ' + refs) .last -- i '] .refval = r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
is_array(str, (r ' + refs) .last, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, 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), is_arraytype(st[(r ' + refs) .last -- _type] .type) ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, ∃ i. ¬ i < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i ∧ is_referencevalue(st[(r ' + refs) .last -- i ']) ∧ st[(r ' + refs) .last -- i '] .refval = r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)])]]