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Proof step 130 from proof cyclic-pseq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 9:
¬ (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
Proof step 129:
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), refs0 + r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ is_referencevalue(st[r2 -- fs ']) ∧ (refs0 + r0 ') .first = st[r2 -- fs '] .refval ∧ validrefs(str, refs0 + r0 ', fs .type, 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

Rule argument

[speclemmaarg: , is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st))) ,[st, ty, refs, r, str] → [st, mkclasstype(class), refs0 + r0 ', r2, str] ,F ,cyclic , ,validrefs-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, mkclasstype(class), refs0 + r0 ', r2, str)]]