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Proof step 134 from proof validrefs-all-same (previous step)

st[r0 -- _type] = st0[r0 -- _type], st[r -- i '] = refval(r1), st0[r -- _type] .type = mkarraytype(ty1), st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- i '] = refval(r1), 0 < st0[r -- _length] .intval, 0 ≤ i, is_array(str, r, st0), is_array(str, r, st), mkarraytype(ty1) ≤ ty, i < st0[r -- _length] .intval, validrefs(str, r1 ' + refs, ty1, st), is_classtype(st0[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st0[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk]), is_arraytype(st0[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i ']), ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '], r0 = r1 ∨ r0 ∈ refs ⊦ is_arraytype(st0[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (0 ≤ i0 ∧ i0 < st[r0 -- _length] .intval → st[r0 -- i0 '] = st0[r0 -- i0 ']), r = jvmref, r0 = jvmref, validrefs(str, r1 ' + refs, ty1, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 133:
st[r0 -- _type] = st0[r0 -- _type], st[r -- i '] = refval(r1), st0[r -- _type] .type = mkarraytype(ty1), st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- i '] = refval(r1), st[r0 -- _length] = st0[r0 -- _length], is_arraytype(st0[r0 -- _type] .type), 0 < st0[r -- _length] .intval, 0 ≤ i, is_array(str, r, st0), is_array(str, r, st), mkarraytype(ty1) ≤ ty, i < st0[r -- _length] .intval, validrefs(str, r1 ' + refs, ty1, st), i0 < st0[r0 -- _length] .intval, 0 ≤ i0, 0 < st0[r0 -- _length] .intval, ∀ r0. (r0 = r ∨ r0 = r1 ∨ r0 ∈ refs) ∧ r0 ≠ jvmref → st[r0 -- _type] = st0[r0 -- _type] ∧ (is_classtype(st[r0 -- _type] .type) → (∀ sk. sk ∈ instfields(st[r0 -- _type] .type .class) → st[r0 -- sk] = st0[r0 -- sk])) ∧ ( is_arraytype(st[r0 -- _type] .type) → st[r0 -- _length] = st0[r0 -- _length] ∧ (∀ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '])), ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '], r0 = r1 ∨ r0 ∈ refs, ∀ i. ¬ i < 0 ∧ ¬ st0[r0 -- _length] .intval ≤ i → st[r0 -- i '] = st0[r0 -- i '] ⊦ r = jvmref, r0 = jvmref, st[r0 -- i0 '] = st0[r0 -- i0 '], validrefs(str, r1 ' + refs, ty1, st0)

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)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]