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Proof step 30 from proof unchNorec-isarray (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = st0[r -- _length], r ∈ 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)), r -- _type ∈ st, unchangedNorec(r, st, st0), r -- _type ∈ st0, r ∈ st0, ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '] ⊦ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
st[r -- _length] = st0[r -- _length], st0[r -- _type] = typeval(mkarraytype(ty)), st[r -- _type] = typeval(mkarraytype(ty)), 0 ≤ st0[r -- _length] .intval, r ∈ st0, r -- _type ∈ st0, unchangedNorec(r, st, st0), r -- _type ∈ st, is_arrayref(r, st0[r -- _length] .intval, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty), st), r ∈ st, is_integervalue(st0[r -- _length]), r -- _length ∈ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty), ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '] ⊦ r = jvmref, (0 ≤ j ∧ j < st0[r -- _length] .intval → okval(st0[r -- j '], ty)) ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ okreftype(refval(r), mkarraytype(ty), st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ is_integervalue(noval)], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]