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Proof step 5 from proof addarray-mode (previous step)

_mode ∈ (st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(0)]), ∀ st, ty, r, vals0. # vals0 < # [] → (_mode ∈ addarray(r, ty, vals0, st) → r = jvmref ∨ _mode ∈ st) ⊦ r = jvmref, _mode ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st

Rule argument

[speclemmaarg: ,rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st ,[val, rk0, st, rk] → [intval(0), r -- _length, st[r -- _type, typeval(mkarraytype(ty))], _mode] ,F ,store ,javastore ,In-insert ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _mode ≠ r -- _length], [CSIMPSEQ : ⊦ _mode ∈ st[r -- _type, val] ↔ _mode ∈ st])], [EXTRATERMS : (intval(0), r -- _length, st[r -- _type, typeval(mkarraytype(ty))], _mode)]]