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Proof step 8 from proof unchNorec-transitivity (previous step)

st[r -- _type] = st1[r -- _type], st0[r -- _type] = st1[r -- _type], unchangedNorec(r, st, st0), unchangedNorec(r, st0, st1), is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st0[r -- _length] ∧ (∀ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st0[r -- i0 ']), is_classtype(st1[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r -- _type] .type .class) → st[r -- fs '] = st0[r -- fs ']), is_classtype(st1[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r -- _type] .type .class) → st0[r -- fs '] = st1[r -- fs ']), is_arraytype(st1[r -- _type] .type) → st0[r -- _length] = st1[r -- _length] ∧ (∀ i0. ¬ i0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ i0 → st0[r -- i0 '] = st1[r -- i0 ']) ⊦ is_arraytype(st1[r -- _type] .type) → st[r -- _length] = st1[r -- _length] ∧ (0 ≤ i ∧ i < st[r -- _length] .intval → st[r -- i '] = st1[r -- i ']), r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st0[r -- _length] = st1[r -- _length], st[r -- _length] = st1[r -- _length], st0[r -- _type] = st1[r -- _type], st[r -- _type] = st1[r -- _type], unchangedNorec(r, st0, st1), unchangedNorec(r, st, st0), is_arraytype(st1[r -- _type] .type), i < st1[r -- _length] .intval, 0 ≤ i, 0 < st1[r -- _length] .intval, ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st0[r -- i0 '] = st1[r -- i0 '], ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st0[r -- i0 '] ⊦ r = jvmref, st[r -- i '] = st1[r -- i ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)])]]