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Proof step 47 from proof validrefs-primarray (previous step)

st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, is_primtype(ty), is_arrayref(r, i, st), r -- _length ∈ st, 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)), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty), ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ mkarraytype(ty) ⊦ r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, is_primtype(ty), is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), st[r -- _type] .type .type ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, is_array(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype (st[r -- _type] .type) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]