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Proof step 75 from proof cyclic-pseq (previous step)

st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), validrefs(str, st[r2 -- fs '] .refval ' + refs + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st), ∀ 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 = st[r2 -- fs '] .refval, r2 = jvmref, r1 = jvmref, validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ' + st[r2 -- fs '] .refval ', st[st[r2 -- fs '] .refval -- _type] .type, st), st[r2 -- fs '] .refval ∈ refs, dups(refs), r2 ∈ refs, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ validrefs(str, refs + r ', ty, st) ∧ st[r -- fs '] .refval = r0 ∧ is_referencevalue(st[r -- fs ']) ∧ is_obj(str, r, st) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) ∧ st[r0 -- _type] .type ≤ fs .type ∧ is_valid_ref(str, r0, st) ∧ type∃(str, st[r0 -- _type] .type) → validrefs(str, refs + r ' + r0 ', ty, st)
Proof step 74:
¬ ( validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st) ∧ st[r2 -- fs '] .refval = st[r2 -- fs '] .refval ∧ is_referencevalue(st[r2 -- fs ']) ∧ is_obj(str, r2, st) ∧ fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ st[st[r2 -- fs '] .refval -- _type] .type ≤ fs .type ∧ is_valid_ref(str, st[r2 -- fs '] .refval, st) ∧ type∃(str, st[st[r2 -- fs '] .refval -- _type] .type)), st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ', fs .type, st), is_obj(str, r2, st), is_obj(str, r1, st1), fs ' ∈ instfields(class), is_referencevalue(st[r2 -- fs ']), validrefs(str, st[r2 -- fs '] .refval ' + refs + r2 ', st[st[r2 -- fs '] .refval -- _type] .type, st), ∀ 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 = st[r2 -- fs '] .refval, r2 = jvmref, r1 = jvmref, validrefs(str, (st[r2 -- fs '] .refval ' + refs) + r2 ' + st[r2 -- fs '] .refval ', st[st[r2 -- fs '] .refval -- _type] .type, st), st[r2 -- fs '] .refval ∈ refs, dups(refs), r2 ∈ refs, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, st[r2 -- fs '] .refval ' + refs, r2, st[st[r2 -- fs '] .refval -- _type] .type, st, fs, st[r2 -- fs '] .refval)]]