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Proof step 23 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, contains(str, st[r -- _type] .type, fs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ contains(str, ty, fs) ↔ type∃(str, ty) ∧ (∃ tys. tys ≠ [] ∧ tys .first ≤ ty ∧ 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))
Proof step 22:
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))

Rule argument

[crewrite-arg: contains-field-def , F , [fs, ty, str] → [fs, st[r -- _type] .type, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (fs, st[r -- _type] .type, str)]]