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Proof step 22 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 ') ⊦ r = r0, r0 = jvmref, r = jvmref, type∃(str, st[r -- _type] .type) ∧ (∃ tys. tys ≠ [] ∧ tys .first ≤ st[r -- _type] .type ∧ contains(str, tys) ∧ is_reftype(tys .last) ∧ (is_classtype(tys .last) → ¬ interface∃(str, tys .last .class) ∧ fs ' ∈ instfields(tys .last .class)) ∧ (is_arraytype(tys .last) → fs ' = _length))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
⊦ ¬ type∃(str, ty) → ¬ contains(str, ty ' + tys)
Proof step 21:
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, ∃ tys0. tys0 ≠ [] ∧ tys0 .first ≤ st[r -- _type] .type ∧ contains(str, tys0) ∧ is_reftype(tys0 .last) ∧ (is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ _length ∈ instfields(tys0 .last .class))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])]]