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Proof step 39 from proof isarray-update (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st ⊦ r = jvmref, r = r0, is_typevalue(typeval(mkarraytype(ty))) ∧ is_arraytype(typeval(mkarraytype(ty)) .type) ∧ typeval(mkarraytype(ty)) .type .type ≤ ty ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 38:
st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, is_integervalue(st[r -- _length]), 0 ≤ st[r -- _length] .intval ⊦ r = jvmref, r = r0, is_arrayref(r, st[r -- _length] .intval, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))])]]