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Proof step 90 from proof pseq-sym-01 (previous step)

st[r -- fs0 '] = refval(jvmref), st1[r1 -- _type] .type = mkclasstype(class), st[r -- _type] = st1[r1 -- _type], fs0 ' ∈ instfields(class), is_valid_ref(str, r1, st1), ∀ 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), ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → ( true → ( ¬ cyclic(str0, r, st) ∧ ¬ cyclic(str0, r0, st0) ∧ ¬ junkref(str0, r, st) ∧ ¬ junkref(str0, r0, st0) → (ps=(r, st, r0, st0) → ps=(r0, st0, r, st)))) ⊦ r1 = jvmref, r = jvmref, st1[r1 -- fs0 '] = refval(jvmref), cyclic(str, r, st), cyclic(str, r1, st1), junkref(str, r, st), junkref(str, r1, st1), is_referencevalue(st1[r1 -- fs0 '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ 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))))
Proof step 89:
is_obj(str, r1, st1), st[r -- fs0 '] = refval(jvmref), st1[r1 -- _type] .type = mkclasstype(class), st[r -- _type] = st1[r1 -- _type], fs0 ' ∈ instfields(class), is_valid_ref(str, r1, st1), ∀ 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), ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → ( true → ( ¬ cyclic(str0, r, st) ∧ ¬ cyclic(str0, r0, st0) ∧ ¬ junkref(str0, r, st) ∧ ¬ junkref(str0, r0, st0) → (ps=(r, st, r0, st0) → ps=(r0, st0, r, st)))) ⊦ r1 = jvmref, r = jvmref, st1[r1 -- fs0 '] = refval(jvmref), cyclic(str, r, st), cyclic(str, r1, st1), junkref(str, r, st), ∃ fs. fs ' ∈ instfields(st1[r1 -- _type] .type .class) ∧ is_referencevalue(st1[r1 -- fs ']) ∧ st1[r1 -- fs '] .refval ≠ jvmref ∧ (¬ st1[st1[r1 -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st1[r1 -- fs '] .refval, st1)), is_referencevalue(st1[r1 -- fs0 '])

Rule argument

[speclemmaarg: , is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ 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)))) ,[st, r, str] → [st1, r1, str] ,F ,junkrefs , ,junkref-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ st[r -- _type] .type = mkclasstype(class) → ¬ is_array(str, r, st)])], [EXTRATERMS : (st1, r1, str)]]