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Proof step 12 from proof isobj-put-index-01 (previous step)

st[r0 -- _type] = typeval(mkclasstype(class)), r0 -- _type ∈ st, r0 ∈ st ⊦ r0 = jvmref, (∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st[r0 -- i ', val])) ↔ (∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st))

User applied rule case distinction

And obtained the following new goals

Proof step 8:
∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st[r0 -- i ', val]), st[r0 -- _type] = typeval(mkclasstype(class)), r0 -- _type ∈ st, r0 ∈ st ⊦ ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st), r0 = jvmref
Proof step 11:
∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st), st[r0 -- _type] = typeval(mkclasstype(class)), r0 -- _type ∈ st, r0 ∈ st ⊦ ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r0, sk, st[r0 -- i ', val]), r0 = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]