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Proof step 8 from proof subset-len (previous step)

r ∈ st, okarray(r, ty, st), r -- _length ∈ st → r -- _length ∈ st0 ∧ st[r -- _length] = st0[r -- _length], ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, st0[r -- _length] .intval = st[r -- _length] .intval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 6:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 7:
⊦ oktype(val, ty, st) ↔ okval(val, ty)

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st, ty, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])], [EXTRATERMS : (st, ty, r)]]