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Proof step 20 from proof isarray-put (previous step)

st[r1 -- _type] = typeval(mkarraytype(ty0)), okval(val, ty), okreftype(refval(r1), mkarraytype(ty0), st) ∧ r1 ≠ jvmref ∧ r1 -- _length ∈ st ∧ is_integervalue(st[r1 -- _length]) ∧ 0 ≤ st[r1 -- _length] .intval ∧ is_arrayref(r1, st[r1 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r1 -- _length] .intval → oktype(st[r1 -- j '], ty0, st)), r1 -- _type ∈ st, r1 ∈ st ⊦ r1 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ r1 -- _length ∈ st ∧ is_integervalue(st[r1 -- _length]) ∧ is_arrayref(r1, st[r1 -- _length] .intval, st) ∧ (0 ≤ j ∧ j < st[r1 -- _length] .intval → okval(st[r1 -- j '], ty0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 13:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 19:
st[r1 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ st[r1 -- _length] .intval, okval(val, ty), r1 ∈ st, r1 -- _type ∈ st, is_arrayref(r1, st[r1 -- _length] .intval, st), is_integervalue(st[r1 -- _length]), r1 -- _length ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ r1 = jvmref, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ (0 ≤ j ∧ j < st[r1 -- _length] .intval → okval(st[r1 -- j '], ty0))

Rule argument

[emptyarg]

Additional information

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