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Proof step 12 from proof isarray-put-field (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, r ∈ st[r0 -- fs ', val], r -- _type ∈ st, r -- _length ∈ st, is_arrayref(r, i, st), r -- _length ∈ st[r0 -- fs ', val], r -- _type ∈ st[r0 -- fs ', val], ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ fs ' = _type, fs ' = _length, r = jvmref, (0 ≤ j ∧ j < i → okval(st[r -- j '], ty)) ∧ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r) .refval -- _type]) ∧ st[refval(r) .refval -- _type] .type ≤ mkarraytype(ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st[r0 -- fs ', val], r -- _length ∈ st[r0 -- fs ', val], is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st, r ∈ st[r0 -- fs ', val], r ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, fs ' = _length, fs ' = _type, okval(st[r -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]