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Proof step 72 from proof unchanged-junkrefs-level (previous step)

¬ ( ¬ ( st[r1 -- _type] = st1[r1 -- _type] ∧ (is_classtype(st[r1 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) → st[r1 -- fs '] = st1[r1 -- fs '])) ∧ ( is_arraytype(st[r1 -- _type] .type) → st[r1 -- _length] = st1[r1 -- _length] ∧ (∀ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval → st[r1 -- i '] = st1[r1 -- i ']))) ∧ r1 ≠ jvmref), st1[r -- _type] = st[r -- _type], st1[r -- i '] = refval(r1), st[r -- _length] = st1[r -- _length], st[r -- _type] .type = mkarraytype(ty1), st[r -- i '] = refval(r1), path∃(str0, r, r1, st1), level⊆(str, str0), unchanged(str0, r, st, st1), junkrefs(str, r1 ' + refs, ty1, st), i < st1[r -- _length] .intval, mkarraytype(ty1) ≤ ty, is_valid_ref(str0, r, st1), is_array(str, r, st1), 0 ≤ i, is_array(str, r, st), unchangedNorec(r, st, st1), is_array(str0, r, st), 0 < st1[r -- _length] .intval, path∃(str0, r, r1, st), unchangedNorec(r1, st, st1), is_valid_ref(str0, r1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st1[r -- i0 '] ⊦ r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), st[r1 -- _type] .type ≤ ty1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
st1[r -- _type] = st[r -- _type], st1[r -- i '] = refval(r1), st[r -- _length] = st1[r -- _length], st[r -- _type] .type = mkarraytype(ty1), st[r -- i '] = refval(r1), st[r1 -- _type] = st1[r1 -- _type], path∃(str0, r, r1, st1), level⊆(str, str0), unchanged(str0, r, st, st1), junkrefs(str, r1 ' + refs, ty1, st), i < st1[r -- _length] .intval, mkarraytype(ty1) ≤ ty, is_valid_ref(str0, r, st1), is_array(str, r, st1), 0 ≤ i, is_array(str, r, st), unchangedNorec(r, st, st1), is_array(str0, r, st), 0 < st1[r -- _length] .intval, path∃(str0, r, r1, st), unchangedNorec(r1, st, st1), is_valid_ref(str0, r1, st), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st1[r -- i0 '], is_classtype(st1[r1 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st1[r1 -- _type] .type .class) → st[r1 -- fs '] = st1[r1 -- fs ']), is_arraytype(st1[r1 -- _type] .type) → st[r1 -- _length] = st1[r1 -- _length] ∧ (∀ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 → st[r1 -- i0 '] = st1[r1 -- i0 ']) ⊦ r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), st1[r1 -- _type] .type ≤ ty1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]