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Proof step 19 from proof isarray-put (previous step)

st[r1 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ st[r1 -- _length] .intval, okval(val, ty), r1 ∈ st, r1 -- _type ∈ st, is_arrayref(r1, st[r1 -- _length] .intval, st), is_integervalue(st[r1 -- _length]), r1 -- _length ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ r1 = jvmref, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ (0 ≤ j ∧ j < st[r1 -- _length] .intval → okval(st[r1 -- j '], ty0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
st[r1 -- _length] = intval(i), st[r1 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, okval(val, ty), r1 ∈ st, r1 -- _type ∈ st, is_arrayref(r1, i, st), is_integervalue(st[r1 -- _length]), r1 -- _length ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ r1 = jvmref, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ (0 ≤ j ∧ j < i → okval(st[r1 -- j '], ty0))

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [st[r1 -- _length], i] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r1 -- _length], i)]]