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Proof step 22 from proof okarray-put-samefield-01 (previous step)

okarray(r, 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ okarray(r, ty, st) ↔ 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))
Proof step 21:
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))

Rule argument

[crewrite-arg: okarrayNotNull , F , [st, ty, r] → [st[r -- mkfs(class, ty0, fieldvar) ', val], ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', val], ty, r)]]