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Proof step 25 from proof okarray-08 (previous step)

st[r0 -- _type] .type .type = int_type, r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), is_integervalue(val), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), 0 ≤ st[r0 -- _length] .intval, r0 ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j1 → is_integervalue(st[r0 -- j1 ']) ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(int_type), st[r0 -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_integervalue(st[r0 -- j ', val][r0 -- j0 ']))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
st[r0 -- _type] .type = mkarraytype(ty), ty = int_type, r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), is_integervalue(val), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), 0 ≤ st[r0 -- _length] .intval, r0 ∈ st, ∀ j1. ¬ j1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j1 → is_integervalue(st[r0 -- j1 ']) ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(int_type), st[r0 -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_integervalue(st[r0 -- j ', val][r0 -- j0 ']))

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r0 -- _type] .type, ty] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r0 -- _type] .type, ty)]]