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Proof step 15 from proof okarray-okarray (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(st[r -- _length] .intval), 0 ≤ st[r -- _length] .intval, r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, is_integervalue(st[r -- _length]) ∧ (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 10:
is_integervalue(val) ⊦ intval(val .intval) = val
Proof step 14:
is_integervalue(st[r -- _length]), st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = st[r -- _length], 0 ≤ st[r -- _length] .intval, r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, is_integervalue(st[r -- _length]) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Rule argument

[speclemmaarg: is_integervalue(val) ,intval(val .intval) = val ,[val] → [st[r -- _length]] ,F ,javavalue , ,intval ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ is_integervalue(intval(i))])], [EXTRATERMS : (st[r -- _length])]]