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Proof step 10 from proof addarray-refs (previous step)

⊦ r0 ∈ addarray(r, initial_value(ty), i, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) ↔ r0 = r ∨ r0 ∈ st .refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (r ∈ addarray(r0, val, i, st) ↔ r ∈ st)
Proof step 5:
⊦ r ≠ r0 → (r ∈ addarray(r0, val, i, st) ↔ r ∈ st)
Proof step 6:
⊦ r ∈ addarray(r, val, i, st) ↔ 0 < i ∨ r ∈ st
Proof step 9:
r0 ≠ r ⊦ r0 ∈ (st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) ↔ r0 = r ∨ r0 ∈ st .refs

Rule argument

[crewrite-arg: in-1dim-04 , F , [st, i, val, r0, r] → [st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)], i, initial_value(ty), r, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(i) ], i, initial_value(ty), r, r0)]]