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Proof step 3 from proof newref-put (conclusion)

⊦ newref(r, st[rk, val]) ↔ newref(r, st) ∧ r ≠ rk .ref

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ newref(r, st[r0 -- sk, val]) ↔ r ≠ r0 ∧ newref(r, st)
Proof step 2:
⊦ newref(r, st) ↔ r ≠ jvmref ∧ (∀ rk. rk ∈ st → rk .ref ≠ r)

Rule argument

[VARWITHVARSEQSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;], [CSIMPSEQ : ⊦ (r -- sk) .ref = r])]]