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Proof step 20 from proof nopathex-badarrayfield (previous step)

fs ' = _length, is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', st[r -- _type] .type, st), is_arraytype(st[r0 -- _type] .type), contains(str, st[r -- _type] .type ' + tys + st[r0 -- _type] .type '), type∃(str, st[r -- _type] .type) ⊦ r = r0, r0 = jvmref, r = jvmref, st[r -- _type] .type ' + tys + st[r0 -- _type] .type ' ≠ [] ∧ (st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') .first ≤ st[r -- _type] .type ∧ contains(str, st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') ∧ is_reftype((st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') .last) ∧ ( is_classtype((st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') .last) → ¬ interface∃(str, (st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') .last .class) ∧ _length ∈ instfields((st[r -- _type] .type ' + tys + st[r0 -- _type] .type ') .last .class))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
fs ' = _length, is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', st[r -- _type] .type, st), is_arraytype(st[r0 -- _type] .type), contains(str, st[r -- _type] .type ' + tys + st[r0 -- _type] .type '), type∃(str, st[r -- _type] .type) ⊦ r = r0, r0 = jvmref, r = jvmref, is_reftype(st[r0 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ (ty ' + tys + ty0 ') .last = ty0], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (ty ' + tys) .first = ty], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])]]