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Proof step 10 from proof exactarray-new (previous step)

newref(r, st), exactarray(refval(r), ty, st[r -- _length] .intval, st[rk, val]) ⊦ r -- _length = rk, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ exactarray(val, ty, i, st) ↔ exactreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ is_arrayref(val .refval, i, st)
Proof step 9:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)

Rule argument

[crewrite-arg: exactarray-01 , F , [st, i, ty, val] → [st[rk, val], st[r -- _length] .intval, ty, refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (st[rk, val], st[r -- _length] .intval, ty, refval(r))]]