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Proof step 18 from proof okarray-put-okval-01 (previous step)

st[r0 -- _length] = intval(j), st[r0 -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r0, j, st), okval(val0, ty), r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, 0 ≤ j, r0 ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty), r0 ≠ r ∨ j0 ≠ i ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(ty), st[r -- i ', val0]) ∧ is_arrayref(r0, j, st[r -- i ', val0]) ∧ (0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 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 17:
st[r0 -- _length] = intval(j), st[r0 -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r0, j, st), okval(val0, ty), r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, 0 ≤ j, r0 ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty), r0 ≠ r ∨ j0 ≠ i ⊦ r0 = jvmref, is_referencevalue(refval(r0)) ∧ ( refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st[r -- i ', val0] ∧ is_typevalue(st[r -- i ', val0][refval(r0) .refval -- _type]) ∧ (st[r -- i ', val0][refval(r0) .refval -- _type]) .type ≤ mkarraytype(ty)) ∧ is_arrayref(r0, j, st[r -- i ', val0]) ∧ (0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st[r -- i ', val0], mkarraytype(ty), refval(r0)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', val0], mkarraytype(ty), refval(r0))]]