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Proof step 12 from proof is_valid_ref-putbytearray (previous step)

st[r0 -- _type] .type ≤ ty, is_arraytype(st[r0 -- _type] .type) ⊦ ty = mkclasstype(`java.lang.Object' .class), is_valid_ref(r0, putByteArray(bytes, r, i, st)) ∧ is_array(str, r0, putByteArray(bytes, r, i, st)) ↔ is_array(str, r0, st), is_arraytype(ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_arraytype(ty) ↔ (∃ ty0. ty = mkarraytype(ty0))
Proof step 11:
st[r0 -- _type] .type ≤ ty, ∃ ty0. st[r0 -- _type] .type = mkarraytype(ty0) ⊦ ty = mkclasstype(`java.lang.Object' .class), is_valid_ref(r0, putByteArray(bytes, r, i, st)) ∧ is_array(str, r0, putByteArray(bytes, r, i, st)) ↔ is_array(str, r0, st), is_arraytype(ty)

Rule argument

[x0lemmaarg: spec-name: javatype instance-name: lemma-name: ex-02 antecedent: succedent: is_arraytype(ty) ↔ (∃ ty0. ty = mkarraytype(ty0)) substlist: [ty] → [st[r0 -- _type] .type] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- _type] .type)]]