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Proof step 36 from proof okarray-onlymod (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), onlyModified(r0, st, st0), r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), st[r -- _type] .type .type ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = r0, r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty)) ∧ st0[r -- _length] = st[r -- _length] ∧ r -- _length ∈ st0 ∧ okreftype(refval(r), mkarraytype(ty), st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
st[r -- _type] .type = mkarraytype(ty0), st[r -- _length] = intval(st[r -- _length] .intval), onlyModified(r0, st, st0), r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = r0, r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty)) ∧ st0[r -- _length] = st[r -- _length] ∧ r -- _length ∈ st0 ∧ okreftype(refval(r), mkarraytype(ty), st0)

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty0] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty0)]]