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Proof step 13 from proof isobj-subset (previous step)

st1[r -- _type] = typeval(mkclasstype(class)), st[r -- _type] = typeval(mkclasstype(class)), is_fskey(sk), r -- _type ∈ st, r -- _type ∈ st1, r ∈ st, r ∈ st1, sk ∈ instfields(class), r -- sk ∈ st, okval(st[r -- sk], sk .fs .type), ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st), ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk] ⊦ r = jvmref, r -- sk ∈ st1 ∧ okval(st1[r -- sk], sk .fs .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
sk = fs ', st1[r -- _type] = typeval(mkclasstype(class)), st[r -- _type] = typeval(mkclasstype(class)), is_fskey(sk), r -- _type ∈ st, r -- _type ∈ st1, r ∈ st, r ∈ st1, sk ∈ instfields(class), r -- sk ∈ st, okval(st[r -- sk], fs .type), ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st), ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk] ⊦ r = jvmref, r -- sk ∈ st1 ∧ okval(st1[r -- sk], fs .type)

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]