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Proof step 46 from proof addarray-identity (previous step)

st[r -- _type] .type = mkarraytype(ty), is_array(r, st), rk ∈ addarray(r, ty, getarray(r, st), st) ⊦ rk .ref = r, rk ∈ st

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r0, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r0, sk)]]