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Proof step 4 from proof in-init-06 (previous step)

r -- fs ' ∈ (st[r0 -- _type, typeval(mkarraytype(ty))][r0 -- _length, intval(n→i(# vals))]), r ∈ (st[r0 -- _type, typeval(mkarraytype(ty))][r0 -- _length, intval(n→i(# vals))]) ⊦ fs ' = _type, fs ' = _length, r -- fs ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ≠ rk0 → (rk ∈ st[rk0, val] ↔ rk ∈ st)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (rk ∈ st[rk0, val] ↔ rk ∈ st) ,[val, rk0, st, rk] → [intval(n→i(# vals)), r0 -- _length, st[r0 -- _type, typeval(mkarraytype(ty))], r -- fs '] ,F ,store ,javastore ,in-neq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (intval(n→i(# vals)), r0 -- _length, st[r0 -- _type, typeval(mkarraytype(ty))], r -- fs ')]]