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Proof step 22 from proof unchanged-lookup-generic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
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]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i])]]