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Proof step 21 from proof unchanged-lookup-generic (previous step)

st[r0 -- _type] = st0[r0 -- _type], path∃(str, r, r0, st), path∃(str, r, r0, st0), is_arraytype(st0[r0 -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval, is_classtype(st0[r0 -- _type] .type) → sk ∈ instfields(st0[r0 -- _type] .type .class), is_classtype(st0[r0 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) → st[r0 -- fs '] = st0[r0 -- fs ']), 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 = jvmref, st[r0 -- sk] = st0[r0 -- sk]

User applied rule cut formula

And obtained the following new goals

Proof step 7:
is_arraytype(st0[r0 -- _type] .type), st[r0 -- _type] = st0[r0 -- _type], path∃(str, r, r0, st), path∃(str, r, r0, st0), is_arraytype(st0[r0 -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval, is_classtype(st0[r0 -- _type] .type) → sk ∈ instfields(st0[r0 -- _type] .type .class), is_classtype(st0[r0 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) → st[r0 -- fs '] = st0[r0 -- fs ']), 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 = jvmref, st[r0 -- sk] = st0[r0 -- sk]
Proof step 20:
st[r0 -- _type] = st0[r0 -- _type], path∃(str, r, r0, st), path∃(str, r, r0, st0), is_arraytype(st0[r0 -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval, is_classtype(st0[r0 -- _type] .type) → sk ∈ instfields(st0[r0 -- _type] .type .class), is_classtype(st0[r0 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) → st[r0 -- fs '] = st0[r0 -- fs ']), 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 ']) ⊦ is_arraytype(st0[r0 -- _type] .type), r0 = jvmref, st[r0 -- sk] = st0[r0 -- sk]

Rule argument

[fma-arg: is_arraytype(st0[r0 -- _type] .type)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (is_arraytype(st0[r0 -- _type] .type))]]