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Proof step 18 from proof okarray-put-samefield-01 (previous step)

st[r -- _type] .type = mkarraytype(ty1), 0 ≤ st[r -- _length] .intval, is_arrayref(r, st[r -- _length] .intval, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ty1 ≤ ty, is_typevalue(st[r -- _type]), r -- _type ∈ st, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, okreftype(refval(r), mkarraytype(ty), st) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
st[r -- _length] = intval(i), st[r -- _type] .type = mkarraytype(ty1), 0 ≤ i, is_arrayref(r, i, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ty1 ≤ ty, is_typevalue(st[r -- _type]), r -- _type ∈ st, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, okreftype(refval(r), mkarraytype(ty), st) ∧ (0 ≤ j ∧ j < i → okval(st[r -- j '], ty))

Rule argument

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

Additional information

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