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Proof step 37 from proof okarray-put-okval (previous step)

okarray(r, ty, st), okval(val, ty), r ∈ st ⊦ r = jvmref, j = i, okreftype(refval(r), mkarraytype(ty), st[r -- i ', val]) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- i ', val]) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- i ', val][r -- j '], ty))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 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 36:
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)), okval(val, ty), r ∈ st ⊦ r = jvmref, j = i, okreftype(refval(r), mkarraytype(ty), st[r -- i ', val]) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- i ', val]) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- i ', val][r -- j '], ty))

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st, ty, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r)]]