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Proof step 16 from proof subset-exactarray (previous step)

st[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st0, r -- _length ∈ st0, 0 ≤ i, r ∈ st, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st0, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, is_arrayref(r, i, st0) ∧ is_referencevalue(refval(r)) ∧ refval(r) .refval ∈ st0 ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∧ is_typevalue(st0[refval(r) .refval -- _type]) ∧ st0[refval(r) .refval -- _type] .type = mkarraytype(ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i), r -- _type ∈ st0, r -- _length ∈ st, is_arrayref(r, i, st), r -- _type ∈ st, r ∈ st, 0 ≤ i, r -- _length ∈ st0, r ∈ st0, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, is_arrayref(r, i, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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))])]]