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Proof step 23 from proof okarray-primput (previous step)

0 < st[r -- _length] .intval, okprimtype(val, ty), j < st[r -- _length] .intval, okarray(refval(r), ty, st[r -- _length] .intval, st), 0 ≤ j ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st[r -- j ', val]) ∧ r -- _length ∈ st ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r -- _length] .intval → oktype((j0 = j ⊃ val; st[r -- j0 ']), ty, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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 22:
0 < st[r -- _length] .intval, okprimtype(val, ty), j < st[r -- _length] .intval, okarray(refval(r), ty, st[r -- _length] .intval, st), 0 ≤ j ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st[r -- j ', val] ∧ is_typevalue(st[r -- j ', val][refval(r) .refval -- _type]) ∧ (st[r -- j ', val][refval(r) .refval -- _type]) .type ≤ mkarraytype(ty)) ∧ r -- _length ∈ st ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- j ', val]) ∧ (0 ≤ j0 ∧ j0 < st[r -- _length] .intval → oktype((j0 = j ⊃ val; st[r -- j0 ']), ty, st))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- j ', val], mkarraytype(ty), refval(r))]]