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Proof step 3 from proof isobj-putref (previous step)

⊦ r ≠ rk .ref → ( r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class)) ∈ st[rk, refval(r)] ∧ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st[rk, refval(r)])) ↔ r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class)) ∈ st ∧ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)))

User applied rule structural induction

And closed the goal!

Rule argument

[VARWITHVARSEQSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r ≠ r0 → ( goodfieldandtype (r, sk, st[r0 -- sk0, val]) ↔ goodfieldandtype(r, sk, st))])]]