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Proof step 35 from proof isarray-update (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, 0 ≤ i ⊦ r = jvmref, r = r0, is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

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