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Proof step 21 from proof okarray-put-samefield-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ 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 9:
⊦ sk0 ≠ _type → (oktype(val, ty, st[r -- sk0, val0]) ↔ oktype(val, ty, st))
Proof step 10:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 20:
r -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), okval(val, ty0), r ∈ st, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), st[r -- _type] .type .type ≤ ty, r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = jvmref, okreftype(refval(r), mkarraytype(ty), st) ∧ (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 : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_arrayref (r, i, st[r0 -- fs ', val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]