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Proof step 9 from proof cyclic-pseq (previous step)

¬ (is_obj(str, r2, st) ∧ st[r2 -- _type] .type ≤ mkclasstype(class)), st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], is_obj(str, r1, st1), validrefs(str, (r2 ' + refs0) + r0 ', mkclasstype(class), st), is_valid_ref(str, r2, st), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[r1 -- fs '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ r2 = jvmref, r1 = jvmref, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), dups(refs0), r2 ∈ refs0, r0 ≠ r2 ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st[r2 -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), validrefs(str, (r2 ' + refs0) + r0 ', mkclasstype(class), st), is_obj(str, r1, st1), is_array(str, r2, st), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[r1 -- fs '], ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ r1 = jvmref, r2 = jvmref, r2 ∈ refs0, dups(refs0), junkref(str, r2, st), junkref(str, r1, st1), cyclic(str, r1, st1), r0 ≠ r2 ∧ ¬ r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ class ≤ class], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2])]]