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Proof step 33 from proof okarray-put-07 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
st[r0 -- _type] .type = mkarraytype(ty0), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), ty0 ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, st[r0 -- _length] .intval, st), j < st[r0 -- _length] .intval, r0 ∈ st, 0 ≤ st[r0 -- _length] .intval, 0 ≤ j, 0 < st[r0 -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r = r0, r0 = jvmref, okval(st[r0 -- j '], ty)

Rule argument

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

Additional information

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