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Proof step 12 from proof isobj-addobj-03 (previous step)

st[r -- _type] = typeval(mkclasstype(class0)), r -- _type ∈ st, r ∈ st ⊦ r = jvmref, r = r0, (∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, addobj(r0, class, fis, st))) ↔ (∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st))

User applied rule case distinction

And obtained the following new goals

Proof step 8:
∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, addobj(r0, class, fis, st)), st[r -- _type] = typeval(mkclasstype(class0)), r -- _type ∈ st, r ∈ st ⊦ ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st), r = jvmref, r = r0
Proof step 11:
∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st), st[r -- _type] = typeval(mkclasstype(class0)), r -- _type ∈ st, r ∈ st ⊦ ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, addobj(r0, class, fis, st)), r = jvmref, r = r0

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]