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Proof step 63 from proof pseq-subset (previous step)

is_obj(str, r, st), st2[r -- fs '] = refval(r2), st1[r1 -- _type] .type = mkclasstype(class), st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], is_obj(str, r, st), is_obj(str, r1, st1), r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, fs ' ∈ instfields(class), ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r = jvmref, r1 = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st)), cyclic(str, r, st), junkref(str, r1, st1), cyclic(str, r1, st1), ps=(r2, st2, st1[r1 -- fs '] .refval, st1), is_referencevalue(st[r -- fs ']), is_reftype(fs .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
st2[r -- _type] = st1[r1 -- _type], st[r -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), st2[r -- fs '] = refval(r2), fs ' ∈ instfields(class), r -- _type ∈ st, r -- _type ∈ st2, r ∈ st, r ∈ st2, is_obj(str, r1, st1), is_obj(str, r, st), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r1 = jvmref, r = jvmref, is_reftype(fs .type), is_referencevalue(st[r -- fs ']), ps=(r2, st2, st1[r1 -- fs '] .refval, st1), cyclic(str, r1, st1), junkref(str, r1, st1), cyclic(str, r, st), ∃ fs0. fs0 ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs0 ']) ∧ st[r -- fs0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs0 '] .refval -- _type] .type ≤ fs0 .type ∨ junkref(str, st[r -- fs0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) .class = class])]]