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Proof step 43 from proof subset-okarray (previous step)

∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk], okarray(r, ty, st), r ∈ st ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ 0 ≤ st0[r -- _length] .intval ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ (∀ j. 0 ≤ j ∧ j < st0[r -- _length] .intval → oktype(st0[r -- j '], ty, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 42:
okarray(r, ty, st), r ∈ st, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ ¬ st0[r -- _length] .intval < 0 ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ (0 ≤ j ∧ j < st0[r -- _length] .intval → okval(st0[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]